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6.2: Identify Adjacent and Vertical Angles

Difficulty Level: At Grade Created by: CK-12
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Adjacent angles are angles that share the same vertex and one common side. If they combine to make a straight line, adjacent angles must add up to 180^{\circ} . The word “adjacent” means “next to” that can help you to remember adjacent angles.


Can you see that angles 1 and 2, whatever their measurements are, will add up to 180^{\circ} ? This is true for angles 3 and 4, because they also form a line. But that’s not all. Angles 1 and 4 also form a line. So do angles 2 and 3. These are also pairs of adjacent angles. Because the adjacent angle pairs form lines, we can also say that they are supplementary. They must add up to 180^{\circ} .

We can find the sums in this way.

\angle{1} + \angle{2} = 180^{\circ}\\\angle{3} + \angle{4} = 180^{\circ}\\








Example A

True or false. Adjacent angles are across from each other.

Solution: False. Adjacent angles are next to each other.

Example B


Solution: True.

Example C

True or false. Adjacent angles can also be vertical angles.

Solution: False.


First identify the vertical angles.





Intersecting lines
lines that cross at one point.
Adjacent Angles
angles that are next to each other and whose sum is 180^{\circ} .
Vertical Angles
angles that are diagonally across from each other and whose sum is 90^{\circ} .
the measure of the space formed by two intersecting lines.

Guided Practice

Here is one for you to try on your own.

Find m\angle 1 .



\angle 1 is vertical angles with 18^\circ , so m\angle 1 = 18^\circ .

This is our answer.

Video Review

Khan Academy Proving Vertical Angles are Equal



1. \angle INK and \angle MNL

2. \angle INJ and \angle NJK

3. \angle MNL and \angle LNK

4. \angle JNL and \angle INM

5. \angle INM and \angle KNL

6. If m\angle INJ = 63^\circ , find m\angle MNL .

Directions: Use this diagram to answer the following questions.

7. True or false. \angle1 and \angle2 are adjacent angles.

8. What is the measure of \angle1 ?

9. What is the measure of \angle2 ?

10. What is the relationship between \angle2 and the angle opposite it?

11. True or false. Adjacent angles 1 and 2 form a straight line with a value of 180^{\circ} .

Directions: Answer true or false for each question.

12. Supplementary angles are also vertical angles.

13. Vertical angles have the same measure.

14. Adjacent angles always have a sum of 180^{\circ} .

15. Adjacent angles are also vertical angles.

16. Adjacent angles are formed when lines intersect.


Adjacent Angles

Adjacent Angles





A diagram is a drawing used to represent a mathematical problem.
Intersecting lines

Intersecting lines

Intersecting lines are lines that cross or meet at some point.
linear pair

linear pair

Vertical Angles

Vertical Angles


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Difficulty Level:

At Grade



Date Created:

Jan 23, 2013

Last Modified:

Feb 26, 2015
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