Vertical Angles

Vertical Angles are the angles opposite each other when two lines cross

"Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.


vertically opposite a and b

Example: a° and b° are vertical angles.

The interesting thing here is that vertical angles are equal:

a° = b°

(in fact they are congruent angles)

Have a play with them yourself. Notice how the 4 angles are actually two pairs of "vertical angles":


Example: Find angles a°, b° and c° below:

vertically opposite b and 40

Because b° is vertically opposite 40°, it must also be 40°

A full circle is 360°, so that leaves 360° − 2×40° = 280°

Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each.

Answer: a = 140°, b = 40° and c = 140°.

Note: They are also called Vertically Opposite Angles, which is just a more exact way of saying the same thing.