WaltonFuture/GeoQA-8K-in-context-synthesizing

images images listlengths 1 1	problem stringlengths 14 524	answer stringclasses 1 value
	<image>Question: If angle 1 measures 60 degrees in the given diagram, what is the measure of angle 2?	NA
	<image>In the given diagram, consider right triangle ABC where angle C equals 90 degrees. The perpendicular bisector of side AB, labeled as DE, intersects BC at point D and intersects AB at point E. If AD divides angle CAB into two angles and the ratio of angle CAD to angle BAD is 0.6, what is the measure of angle ADC?	NA
	<image>Question: In the given figure, line \( l_1 \) is parallel to line \( l_2 \), and triangle \( ABC \) is an equilateral triangle. If angle \( 1 \) measures \( 50^\circ \), what is the measure of angle \( 2 \)?	NA
	<image>In the given triangle ABC, if line BD is perpendicular to AC and also bisects it, and angle C measures 30 degrees, what is the measure of angle ABD?	NA
	<image>In the given diagram, if angle B measures 45° and angle C measures 60°, and MP and QN bisect AB and AC perpendicularly, what is the measure of angle PAQ?	NA
	<image>Question: In the given right triangle ABC with angle ACB being 90 degrees and angle A measuring 52 degrees, a circle centered at point B with radius BC intersects AB at point D. If angle CBD is 38 degrees, what is the measure of angle ADC?	NA
	<image>Question: In triangle ABC, AB = AC, angle BAC measures 120°, AD is the median of side BC, CE bisects angle BCA, and intersects AB at point E, with AD intersecting CE at point F. What is the degree measure of angle CFA?	NA
	<image>In the given illustration, triangle ABC is depicted with BA being equal to BC. The line segment DE serves as the perpendicular bisector of side AB, intersecting BC and AB at points D and E, respectively. If AD functions as the angle bisector of angle BAC, and the measure of angle C is 72°, what is the degree measure of angle B?	NA
	<image>Question: In right triangle ABC, where angle ACB is 90 degrees, an arc is drawn with point C as the center and CB as the radius, intersecting AB at point D. If angle ACD measures 30 degrees, what is the measure of angle A?	NA
	<image>In the given triangle ABC, where AB is equal to AC, and AD is the median of side BC, with angle C measuring 30 degrees, what is the measure of angle CAD?	NA
	<image>Question: In the given figure, the quadrilateral ABCD is inscribed in circle O. If angle A measures 58°, what is the measure of angle BOD?	NA
	<image>Question: In the given figure, if angle BOD measures 120 degrees and angle AOC measures 30 degrees, what is the measure of angle DEB?	NA
	<image>Question: In the given figure, point O is the intersection of AE and CD, with AB being parallel to CD. If OC is equal to OE and angle B measures 60 degrees, what is the measure of angle C?	NA
	<image>In the given diagram, triangle ABC is equilateral with BO as the median line, and BA extended to point D such that AD is equal to AO. If angle AOB measures 60°, what is the degree measure of angle DOB?	NA
	<image>Question: In the given diagram, if AB is parallel to CD and AC equals BC, and angle 1 measures 80 degrees, what is the degree measure of angle 2?	NA
	<image>In the given diagram, point D lies on AC, while point E lies on AB. It is also given that AB is equal to AC, and BC is equal to BD, and AD is equal to DE, which also equals BE. If the measure of angle C is 30 degrees, what is the measure of angle A?	NA
	<image>Question: If triangle ABC is divided into smaller triangles by lines AD and BE, what is the total measure of all the angles formed at point D and point E?	NA
	<image>Question: In the given diagram, triangle ABC has angle ACB measuring 135 degrees. If square ACDE and regular pentagon BCFGH are constructed with sides AC and BC, respectively, what is the measure of angle DCF?	NA
	<image>Question: If Xiaohong folds a square piece of paper into a regular pentagon, what is the measure of angle 1 in the figure?	NA
	<image>Question: In the given diagram, the sides CD and FG of the regular pentagon ABCDE and the regular hexagon EFGHMN are on the line l. The pentagon is on the left side of the hexagon, and both polygons are on the same side of the line l. If the measure of angle CDE is 108°, what is the measure of angle EFG?	NA
	<image>Question: If points A, B, and C lie on circle O and angle ACB measures 50.0 degrees, what is the measure of angle AOB?	NA
	<image>Question: In the given figure, quadrilateral ABCD has AD = BC, and points P, E, and F are the midpoints of diagonals BD, AB, and CD respectively. If angle EPF measures 120 degrees, what is the measure of angle AED?	NA
	<image>Question: In the given figure, pentagon ABCDE is a regular pentagon. If line segment AB is extended to intersect line l2 at point F, and ∠BFE = 144°, what is the measure of ∠2?	NA
	<image>In the parallelogram ABCD, where angle B measures 75 degrees, the angle bisector of angle BAD intersects BC at point E. If the measure of angle AED is 90 degrees, what is the degree measure of angle EAC?	NA
	<image>If points D and E are the midpoints of the sides AB and AC of triangle ABC and connected, and angle B measures 80 degrees while angle C measures 40 degrees, what is the degree measure of angle AED?	NA
	<image>In parallelogram ABCD, if angle ADC measures 140° and angle CAD measures 25°, what is the measure of angle CAB?	NA
	<image>In the given diagram, quadrilateral ABCD is depicted with AE perpendicular to CD. If angle B measures 85 degrees, what is the degree measure of angle DAE?	NA
	<image>In the given diagram depicting quadrilateral ABCD, if angle ADC measures 100 degrees and angle BCD measures 75 degrees, what is the measure of angle BAD?	NA
	<image>Question: If angle B in triangle BCDE measures 50 degrees and DE is parallel to AC, what is the measure of angle E?	NA
	<image>If angle B measures 120 degrees in parallelogram ABCD, what is the degree measure of angle D?	NA
	<image>In the given diagram, if in triangle ABC, point D is the midpoint of AC and point E is the midpoint of AB, and point F lies on the extension of BC, and if angle A measures 40° and angle AED measures 25°, then what is the degree measure of angle ACF?	NA
	<image>In the given diagram of quadrilateral ABCD, the angle bisector BE intersects DC at point E. If angle D measures 120°, what is the measure of angle CEB?	NA
	<image>In parallelogram ABCD, if BD = BC and AE is perpendicular to BD at point E, with angle C = 60°, what is the measure of angle DAB?	NA
	<image>Question: If the sum of angles B and D in parallelogram ABCD is 230 degrees, what is the measurement of angle A?	NA
	<image>If angle C in the parallelogram ABCD is 110 degrees, what is the measure of angle A?	NA
	<image>In the given parallelogram ABCD, if the sum of angles A and D equals 120°, what is the measure of angle B?	NA
	<image>In the given parallelogram ABCD, if the sum of angle A and angle C measures 260°, what is the measure of angle B?	NA
	<image>In the given figure, if in quadrilateral ABCD, angle A added to angle C equals 180 degrees, what is the measure of angle B?	NA
	<image>In parallelogram ABCD, if angle DBC measures 30° and angle ADC measures 120°, what is the measure of angle BCD?	NA
	<image>If the sum of angle 1, angle 2, and angle 3 is 280.0 degrees as indicated in the figure, what is the measure of angle 4?	NA
	<image>In the parallelogram ABCD, if angle B measures 30 degrees, what is the degree measure of angle D?	NA
	<image>In the given diagram illustrating quadrilateral ABCD, if the sum of angle A and angle C is 160 degrees, what is the measure of angle B?	NA
	<image>In the given diagram of quadrilateral ABCD, where AB equals BD and point E lies on BD with CE measuring the same as CB, if angle ADB is 65 degrees, what would be the measure of angle BCD?	NA
	<image>In the given diagram, for the quadrilateral ABCD, a point M is positioned on the extension of side AB. If angle D measures 120 degrees and angle A measures 60 degrees, what is the measure of angle CBM?	NA
	<image>In the given figure, if the sum of angles A and D in quadrilateral ABCD is 130 degrees, what is the measure of angle B?	NA
	<image>Question: In quadrilateral ABCD, point E lies on the extension of side DC, AE equals DE, and angle E measures 46 degrees. If angle BAC is 30 degrees, what is the measure of angle D?	NA
	<image>In the given parallelogram ABCD, if angle B measures 45°, what is the measure of angle D?	NA
	<image>Question: If the measure of angle B in parallelogram ABCD is 70 degrees, what is the measure of angle D?	NA
	<image>Question: In parallelogram ABCD, if angle B measures 120° and angle D measures 60°, what is the measure of angle 1?	NA
	<image>Question: In the same figure showing a set of triangular plates with their right-angle vertices coinciding, if angle AOB measures 120.0 degrees, what is the measure of angle COD?	NA
	<image>In parallelogram ABCD, point E lies on side BC, and the line segment AE is drawn. If AE bisects angle BAD and angle D measures 62 degrees, what is the measure of angle AEC?	NA
	<image>Question: In the given diagram of triangle ABC where AB is equal to AC, point D lies on side AC. If angle A measures 40° and angle BCD measures 110°, what is the degree measure of angle E?	NA
	<image>Question: In parallelogram ABCD, extend side AD to point F such that AF = AD. If angle 1 measures 70°, what is the measure of angle B?	NA
	<image>In the given diagram, ABCD forms a parallelogram. At point E, DE is perpendicular to BC, and at point F, BF is perpendicular to CD. If DE and BF intersect at point H, and angle A measures 75°, then what is the measure of angle EHF?	NA
	<image>In the given diagram, the quadrilateral ABCD is depicted. If the measure of angle B is 80 degrees and AD is extended to point F, what is the measure of angle DCF?	NA
	<image>If triangle ABC has angle B measuring 80 degrees and angle C measuring 40 degrees, and points D, E, and F are the midpoints of sides AB, BC, and CA respectively, what is the measure of angle DEF?	NA
	<image>In parallelogram ABCD, if angle A is 70°, what is the measure of angle C?	NA
	<image>Question: In the given figure, the perpendicular bisector of BC intersects AB and BC at points D and E, respectively. It also connects CD. If angle B measures 25.0 degrees and angle ACD is twice the measure of angle B, what is the degree measure of angle ACD?	NA
	<image>In the same triangle ABC, if angle A measures 30 degrees and angle B measures 60 degrees, what is the measure of angle C?	NA
	<image>Question: If two protractors are placed such that their zero-degree lines overlap and one protractor is rotated 30° clockwise relative to the other, what is the measure of the angle formed between the outer edges of the protractors?	NA
	<image>Question: In the given triangle ABC, with angles A, B, and C measuring 20°, 45°, and 35° respectively, point D lies on side AC such that AD = DC. If line segment BE intersects AD at point F, what is the measure of angle DFE?	NA
	<image>In the given diagram, if triangle ABC is folded along DE and point A ends up inside quadrilateral BCDE, with angle 1 measuring 60° and angle 2 measuring 130°, what is the measure of angle A?	NA
	<image>In the given diagram, BD is the angle bisector of triangle ABC. If angle ABD is 45 degrees and angle BDC is 75 degrees, what is the measure of angle C?	NA
	<image>Question: If angle A measures 45° and angle D measures 75°, what is the measure of angle B in the given diagram?	NA
	<image>Question: BP is the bisector of angle ABC, CP is the bisector of the adjacent supplementary angle of angle ACB. If angle ABP = 30° and angle ACP = 70°, find the measure of angle P.	NA
	<image>Question: If a triangle ruler with a 45.0-degree angle is placed on the ruler and angle 1 measures 30.0 degrees in the given figure, what is the measure of angle 2?	NA
	<image>Question: If the sum of angles A and B in triangle ABC is 115°, what is the measure of angle C?	NA
	<image>Question: In the given figure, if angle A measures 75° and angle B measures 45°, what is the sum of the degrees of angles D, E, F, and G?	NA
	<image>In the given heptagon ABCDEFG, the lines EF and BA are extended to intersect at point P. If the total of the exterior angles of angles ABC, BCD, CDE, and DEF is 170°, what is the measurement of angle P?	NA
	<image>In the provided diagram, if angle A measures 60°, angle B measures 50°, and angle C measures 70°, what is the total measure of angles D and E?	NA
	<image>Question: In the given diagram, points B, C, and D are aligned in a straight line. If angle B measures 74° and angle ACD measures 130°, what is the measure of angle A?	NA
	<image>Question: In triangle ABC, the angle bisectors of angles B and C intersect at point O. If angle A measures 70°, what is the measure of angle BOC?	NA
	<image>Question: In the triangle board puzzle activity, if angle ABC measures 75° and angle ACB measures 45°, what is the measure of angle α?	NA
	<image>Question: In the given diagram, circle O has chord AB and tangent AC with point A as the tangent point. Additionally, line BC passes through the center of the circle. If angle B measures 30.0 degrees, what is the measure of angle C?	NA
	<image>Question: In the same grid diagram, if point B is moved to the right by two units and down by one unit, what would be the new coordinates of point B?	NA
	<image>Question: In the given diagram, if BD is the diameter of circle O, and BD is perpendicular to AC at point E, with angle AOC measuring 120 degrees, what is the measure of angle ODC?	NA
	<image>If AB is a chord of circle O and angle BOC measures 116 degrees, what is the measure of angle A?	NA
	<image>Question: In the given figure, triangle ABC is inscribed in circle O, with angle A measuring 60°. If point D lies on arc BC and angle BDC measures 30°, what is the measure of angle BCO?	NA
	<image>In the given diagram, if angle C in circle O measures 30 degrees and angle B is 45 degrees, what is the measure of angle A?	NA
	<image>Question: In the given diagram, if AB is the diameter of circle O and points C, D, and E are located on circle O, with AD equal to CD and angle E measuring 70°, what is the measure of angle ADE?	NA
	<image>In the given diagram, if triangle ABC is inscribed in circle O and the measure of angle ABO is 60 degrees, what is the measure of angle ACB?	NA
	<image>If quadrilateral ABCD is circumscribed around circle O and one of its interior angles, angle ADC, measures 120°, then what is the measure of the other interior angle, angle ABC?	NA
	<image>Question: In the given diagram, all the points A, B, C, D, and P are located on the circle O. The line OC is perpendicular to AB. If angle ADC measures 20° (where 0° < α < 90°), what is the measure of angle APB?	NA
	<image>Question: If the slant height of the conical funnel made by Xiao Ming is 10.0 cm, what is the volume of the funnel?	NA
	<image>Question: In the given diagram, AB is the diameter of circle O, and points C and D lie on circle O. If angle B measures 60°, what is the measure of angle ACD?	NA
	<image>Question: If CD is the diameter of circle O and chord DE is parallel to radius OB, while arc AE measures 104 degrees, what is the measure of angle A?	NA
	<image>If point A, B, and C are on circle O and angle BAC measures 32 degrees, what is the measure of angle OBC?	NA
	<image>Question: In the provided diagram, points A, B, and C lie on the circle O in the given order. If the measure of angle ACB is 50 degrees, what is the measure of angle AOB?	NA
	<image>Question: In the given figure with points A, B, C, D, and E all lying on circle O, and AC equal to AE, if angle B measures 128 degrees, what is the degree measure of angle C?	NA
	<image>Question: In the given circle with center O, points A, B, and C lie on the circumference. If angle AOC measures 120°, what is the measure of angle ABC?	NA
	<image>In the given diagram, if quadrilateral ABCD is inscribed in circle O and angle A measures 60°, what is the degree measure of angle BOD?	NA
	<image>Question: If points A, B, and C are on circle O, and angle BAC measures 40 degrees, what is the measure of angle BOC?	NA
	<image>Question: In the given circle with center O, AB is the diameter. Points C and D lie on the circumference. Connect AC, CD, and AD. If angle ACD measures 60°, what is the measure of angle BAC?	NA
	<image>Question: In the given diagram, circle O has line AB as its diameter. Point D lies on circle O, and OD and BD are connected. A tangent is drawn to circle O passing through point D, and it intersects the extension of line BA at point C. If angle BOD measures 110°, what is the measure of angle B?	NA
	<image>What is the area of the larger circle if the radius of the smaller circle is 5 meters and the distance between their centers is 10 meters?	NA
	<image>Question: In the given figure, quadrilateral ABCD is inscribed in circle O, with DA = DC. If angle ABE = 30°, find the measure of angle BCD.	NA
	<image>Question: If angle ACB measures 54 degrees and points A, B, and C are all located on circle O, what is the measure of angle AOB?	NA
	<image>Question: In the given figure, circle O is the circumcircle of triangle ABC, and angle A measures 62°. Point E is the midpoint of BC, and line segment OE intersects circle O at point D. If BD is connected, what is the measure of angle BDC?	NA
	<image>In the given diagram of circle O, if the length of AB is equal to the length of AC and angle B measures 80 degrees, what is the measure of angle C?	NA
	<image>Question: If angle BDC measures 120° in the given circle, what is the measure of angle ADE?	NA

<image>Question: If angle 1 measures 60 degrees in the given diagram, what is the measure of angle 2?

NA

<image>In the given diagram, consider right triangle ABC where angle C equals 90 degrees. The perpendicular bisector of side AB, labeled as DE, intersects BC at point D and intersects AB at point E. If AD divides angle CAB into two angles and the ratio of angle CAD to angle BAD is 0.6, what is the measure of angle ADC?

NA

<image>Question: In the given figure, line \( l_1 \) is parallel to line \( l_2 \), and triangle \( ABC \) is an equilateral triangle. If angle \( 1 \) measures \( 50^\circ \), what is the measure of angle \( 2 \)?

NA

<image>In the given triangle ABC, if line BD is perpendicular to AC and also bisects it, and angle C measures 30 degrees, what is the measure of angle ABD?

NA

<image>In the given diagram, if angle B measures 45° and angle C measures 60°, and MP and QN bisect AB and AC perpendicularly, what is the measure of angle PAQ?

NA

<image>Question: In the given right triangle ABC with angle ACB being 90 degrees and angle A measuring 52 degrees, a circle centered at point B with radius BC intersects AB at point D. If angle CBD is 38 degrees, what is the measure of angle ADC?

NA

<image>Question: In triangle ABC, AB = AC, angle BAC measures 120°, AD is the median of side BC, CE bisects angle BCA, and intersects AB at point E, with AD intersecting CE at point F. What is the degree measure of angle CFA?

NA

<image>In the given illustration, triangle ABC is depicted with BA being equal to BC. The line segment DE serves as the perpendicular bisector of side AB, intersecting BC and AB at points D and E, respectively. If AD functions as the angle bisector of angle BAC, and the measure of angle C is 72°, what is the degree measure of angle B?

NA

<image>Question: In right triangle ABC, where angle ACB is 90 degrees, an arc is drawn with point C as the center and CB as the radius, intersecting AB at point D. If angle ACD measures 30 degrees, what is the measure of angle A?

NA

<image>In the given triangle ABC, where AB is equal to AC, and AD is the median of side BC, with angle C measuring 30 degrees, what is the measure of angle CAD?

NA

<image>Question: In the given figure, the quadrilateral ABCD is inscribed in circle O. If angle A measures 58°, what is the measure of angle BOD?

NA

<image>Question: In the given figure, if angle BOD measures 120 degrees and angle AOC measures 30 degrees, what is the measure of angle DEB?

NA

<image>Question: In the given figure, point O is the intersection of AE and CD, with AB being parallel to CD. If OC is equal to OE and angle B measures 60 degrees, what is the measure of angle C?

NA

<image>In the given diagram, triangle ABC is equilateral with BO as the median line, and BA extended to point D such that AD is equal to AO. If angle AOB measures 60°, what is the degree measure of angle DOB?

NA

<image>Question: In the given diagram, if AB is parallel to CD and AC equals BC, and angle 1 measures 80 degrees, what is the degree measure of angle 2?

NA

<image>In the given diagram, point D lies on AC, while point E lies on AB. It is also given that AB is equal to AC, and BC is equal to BD, and AD is equal to DE, which also equals BE. If the measure of angle C is 30 degrees, what is the measure of angle A?

NA

<image>Question: If triangle ABC is divided into smaller triangles by lines AD and BE, what is the total measure of all the angles formed at point D and point E?

NA

<image>Question: In the given diagram, triangle ABC has angle ACB measuring 135 degrees. If square ACDE and regular pentagon BCFGH are constructed with sides AC and BC, respectively, what is the measure of angle DCF?

NA

<image>Question: If Xiaohong folds a square piece of paper into a regular pentagon, what is the measure of angle 1 in the figure?

NA

<image>Question: In the given diagram, the sides CD and FG of the regular pentagon ABCDE and the regular hexagon EFGHMN are on the line l. The pentagon is on the left side of the hexagon, and both polygons are on the same side of the line l. If the measure of angle CDE is 108°, what is the measure of angle EFG?

NA

<image>Question: If points A, B, and C lie on circle O and angle ACB measures 50.0 degrees, what is the measure of angle AOB?

NA

<image>Question: In the given figure, quadrilateral ABCD has AD = BC, and points P, E, and F are the midpoints of diagonals BD, AB, and CD respectively. If angle EPF measures 120 degrees, what is the measure of angle AED?

NA

<image>Question: In the given figure, pentagon ABCDE is a regular pentagon. If line segment AB is extended to intersect line l2 at point F, and ∠BFE = 144°, what is the measure of ∠2?

NA

<image>In the parallelogram ABCD, where angle B measures 75 degrees, the angle bisector of angle BAD intersects BC at point E. If the measure of angle AED is 90 degrees, what is the degree measure of angle EAC?

NA

<image>If points D and E are the midpoints of the sides AB and AC of triangle ABC and connected, and angle B measures 80 degrees while angle C measures 40 degrees, what is the degree measure of angle AED?

NA

<image>In parallelogram ABCD, if angle ADC measures 140° and angle CAD measures 25°, what is the measure of angle CAB?

NA

<image>In the given diagram, quadrilateral ABCD is depicted with AE perpendicular to CD. If angle B measures 85 degrees, what is the degree measure of angle DAE?

NA

<image>In the given diagram depicting quadrilateral ABCD, if angle ADC measures 100 degrees and angle BCD measures 75 degrees, what is the measure of angle BAD?

NA

<image>Question: If angle B in triangle BCDE measures 50 degrees and DE is parallel to AC, what is the measure of angle E?

NA

<image>If angle B measures 120 degrees in parallelogram ABCD, what is the degree measure of angle D?

NA

<image>In the given diagram, if in triangle ABC, point D is the midpoint of AC and point E is the midpoint of AB, and point F lies on the extension of BC, and if angle A measures 40° and angle AED measures 25°, then what is the degree measure of angle ACF?

NA

<image>In the given diagram of quadrilateral ABCD, the angle bisector BE intersects DC at point E. If angle D measures 120°, what is the measure of angle CEB?

NA

<image>In parallelogram ABCD, if BD = BC and AE is perpendicular to BD at point E, with angle C = 60°, what is the measure of angle DAB?

NA

<image>Question: If the sum of angles B and D in parallelogram ABCD is 230 degrees, what is the measurement of angle A?

NA

<image>If angle C in the parallelogram ABCD is 110 degrees, what is the measure of angle A?

NA

<image>In the given parallelogram ABCD, if the sum of angles A and D equals 120°, what is the measure of angle B?

NA

<image>In the given parallelogram ABCD, if the sum of angle A and angle C measures 260°, what is the measure of angle B?

NA

<image>In the given figure, if in quadrilateral ABCD, angle A added to angle C equals 180 degrees, what is the measure of angle B?

NA

<image>In parallelogram ABCD, if angle DBC measures 30° and angle ADC measures 120°, what is the measure of angle BCD?

NA

<image>If the sum of angle 1, angle 2, and angle 3 is 280.0 degrees as indicated in the figure, what is the measure of angle 4?

NA

<image>In the parallelogram ABCD, if angle B measures 30 degrees, what is the degree measure of angle D?

NA

<image>In the given diagram illustrating quadrilateral ABCD, if the sum of angle A and angle C is 160 degrees, what is the measure of angle B?

NA

<image>In the given diagram of quadrilateral ABCD, where AB equals BD and point E lies on BD with CE measuring the same as CB, if angle ADB is 65 degrees, what would be the measure of angle BCD?

NA

<image>In the given diagram, for the quadrilateral ABCD, a point M is positioned on the extension of side AB. If angle D measures 120 degrees and angle A measures 60 degrees, what is the measure of angle CBM?

NA

<image>In the given figure, if the sum of angles A and D in quadrilateral ABCD is 130 degrees, what is the measure of angle B?

NA

<image>Question: In quadrilateral ABCD, point E lies on the extension of side DC, AE equals DE, and angle E measures 46 degrees. If angle BAC is 30 degrees, what is the measure of angle D?

NA

<image>In the given parallelogram ABCD, if angle B measures 45°, what is the measure of angle D?

NA

<image>Question: If the measure of angle B in parallelogram ABCD is 70 degrees, what is the measure of angle D?

NA

<image>Question: In parallelogram ABCD, if angle B measures 120° and angle D measures 60°, what is the measure of angle 1?

NA

<image>Question: In the same figure showing a set of triangular plates with their right-angle vertices coinciding, if angle AOB measures 120.0 degrees, what is the measure of angle COD?

NA

<image>In parallelogram ABCD, point E lies on side BC, and the line segment AE is drawn. If AE bisects angle BAD and angle D measures 62 degrees, what is the measure of angle AEC?

NA

<image>Question: In the given diagram of triangle ABC where AB is equal to AC, point D lies on side AC. If angle A measures 40° and angle BCD measures 110°, what is the degree measure of angle E?

NA

<image>Question: In parallelogram ABCD, extend side AD to point F such that AF = AD. If angle 1 measures 70°, what is the measure of angle B?

NA

<image>In the given diagram, ABCD forms a parallelogram. At point E, DE is perpendicular to BC, and at point F, BF is perpendicular to CD. If DE and BF intersect at point H, and angle A measures 75°, then what is the measure of angle EHF?

NA

<image>In the given diagram, the quadrilateral ABCD is depicted. If the measure of angle B is 80 degrees and AD is extended to point F, what is the measure of angle DCF?

NA

<image>If triangle ABC has angle B measuring 80 degrees and angle C measuring 40 degrees, and points D, E, and F are the midpoints of sides AB, BC, and CA respectively, what is the measure of angle DEF?

NA

<image>In parallelogram ABCD, if angle A is 70°, what is the measure of angle C?

NA

<image>Question: In the given figure, the perpendicular bisector of BC intersects AB and BC at points D and E, respectively. It also connects CD. If angle B measures 25.0 degrees and angle ACD is twice the measure of angle B, what is the degree measure of angle ACD?

NA

<image>In the same triangle ABC, if angle A measures 30 degrees and angle B measures 60 degrees, what is the measure of angle C?

NA

<image>Question: If two protractors are placed such that their zero-degree lines overlap and one protractor is rotated 30° clockwise relative to the other, what is the measure of the angle formed between the outer edges of the protractors?

NA

<image>Question: In the given triangle ABC, with angles A, B, and C measuring 20°, 45°, and 35° respectively, point D lies on side AC such that AD = DC. If line segment BE intersects AD at point F, what is the measure of angle DFE?

NA

<image>In the given diagram, if triangle ABC is folded along DE and point A ends up inside quadrilateral BCDE, with angle 1 measuring 60° and angle 2 measuring 130°, what is the measure of angle A?

NA

<image>In the given diagram, BD is the angle bisector of triangle ABC. If angle ABD is 45 degrees and angle BDC is 75 degrees, what is the measure of angle C?

NA

<image>Question: If angle A measures 45° and angle D measures 75°, what is the measure of angle B in the given diagram?

NA

<image>Question: BP is the bisector of angle ABC, CP is the bisector of the adjacent supplementary angle of angle ACB. If angle ABP = 30° and angle ACP = 70°, find the measure of angle P.

NA

<image>Question: If a triangle ruler with a 45.0-degree angle is placed on the ruler and angle 1 measures 30.0 degrees in the given figure, what is the measure of angle 2?

NA

<image>Question: If the sum of angles A and B in triangle ABC is 115°, what is the measure of angle C?

NA

<image>Question: In the given figure, if angle A measures 75° and angle B measures 45°, what is the sum of the degrees of angles D, E, F, and G?

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<image>In the given heptagon ABCDEFG, the lines EF and BA are extended to intersect at point P. If the total of the exterior angles of angles ABC, BCD, CDE, and DEF is 170°, what is the measurement of angle P?

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<image>In the provided diagram, if angle A measures 60°, angle B measures 50°, and angle C measures 70°, what is the total measure of angles D and E?

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<image>Question: In the given diagram, points B, C, and D are aligned in a straight line. If angle B measures 74° and angle ACD measures 130°, what is the measure of angle A?

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<image>Question: In triangle ABC, the angle bisectors of angles B and C intersect at point O. If angle A measures 70°, what is the measure of angle BOC?

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<image>Question: In the triangle board puzzle activity, if angle ABC measures 75° and angle ACB measures 45°, what is the measure of angle α?

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<image>Question: In the given diagram, circle O has chord AB and tangent AC with point A as the tangent point. Additionally, line BC passes through the center of the circle. If angle B measures 30.0 degrees, what is the measure of angle C?

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<image>Question: In the same grid diagram, if point B is moved to the right by two units and down by one unit, what would be the new coordinates of point B?

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<image>Question: In the given diagram, if BD is the diameter of circle O, and BD is perpendicular to AC at point E, with angle AOC measuring 120 degrees, what is the measure of angle ODC?

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<image>If AB is a chord of circle O and angle BOC measures 116 degrees, what is the measure of angle A?

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<image>Question: In the given figure, triangle ABC is inscribed in circle O, with angle A measuring 60°. If point D lies on arc BC and angle BDC measures 30°, what is the measure of angle BCO?

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<image>In the given diagram, if angle C in circle O measures 30 degrees and angle B is 45 degrees, what is the measure of angle A?

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<image>Question: In the given diagram, if AB is the diameter of circle O and points C, D, and E are located on circle O, with AD equal to CD and angle E measuring 70°, what is the measure of angle ADE?

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<image>In the given diagram, if triangle ABC is inscribed in circle O and the measure of angle ABO is 60 degrees, what is the measure of angle ACB?

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<image>If quadrilateral ABCD is circumscribed around circle O and one of its interior angles, angle ADC, measures 120°, then what is the measure of the other interior angle, angle ABC?

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<image>Question: In the given diagram, all the points A, B, C, D, and P are located on the circle O. The line OC is perpendicular to AB. If angle ADC measures 20° (where 0° < α < 90°), what is the measure of angle APB?

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<image>Question: If the slant height of the conical funnel made by Xiao Ming is 10.0 cm, what is the volume of the funnel?

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<image>Question: In the given diagram, AB is the diameter of circle O, and points C and D lie on circle O. If angle B measures 60°, what is the measure of angle ACD?

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<image>Question: If CD is the diameter of circle O and chord DE is parallel to radius OB, while arc AE measures 104 degrees, what is the measure of angle A?

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<image>If point A, B, and C are on circle O and angle BAC measures 32 degrees, what is the measure of angle OBC?

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<image>Question: In the provided diagram, points A, B, and C lie on the circle O in the given order. If the measure of angle ACB is 50 degrees, what is the measure of angle AOB?

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<image>Question: In the given figure with points A, B, C, D, and E all lying on circle O, and AC equal to AE, if angle B measures 128 degrees, what is the degree measure of angle C?

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<image>Question: In the given circle with center O, points A, B, and C lie on the circumference. If angle AOC measures 120°, what is the measure of angle ABC?

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<image>In the given diagram, if quadrilateral ABCD is inscribed in circle O and angle A measures 60°, what is the degree measure of angle BOD?

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<image>Question: If points A, B, and C are on circle O, and angle BAC measures 40 degrees, what is the measure of angle BOC?

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<image>Question: In the given circle with center O, AB is the diameter. Points C and D lie on the circumference. Connect AC, CD, and AD. If angle ACD measures 60°, what is the measure of angle BAC?

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<image>Question: In the given diagram, circle O has line AB as its diameter. Point D lies on circle O, and OD and BD are connected. A tangent is drawn to circle O passing through point D, and it intersects the extension of line BA at point C. If angle BOD measures 110°, what is the measure of angle B?

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<image>What is the area of the larger circle if the radius of the smaller circle is 5 meters and the distance between their centers is 10 meters?

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<image>Question: In the given figure, quadrilateral ABCD is inscribed in circle O, with DA = DC. If angle ABE = 30°, find the measure of angle BCD.

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<image>Question: If angle ACB measures 54 degrees and points A, B, and C are all located on circle O, what is the measure of angle AOB?

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<image>Question: In the given figure, circle O is the circumcircle of triangle ABC, and angle A measures 62°. Point E is the midpoint of BC, and line segment OE intersects circle O at point D. If BD is connected, what is the measure of angle BDC?

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<image>In the given diagram of circle O, if the length of AB is equal to the length of AC and angle B measures 80 degrees, what is the measure of angle C?

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<image>Question: If angle BDC measures 120° in the given circle, what is the measure of angle ADE?

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