Vertically Opposite Angles

Vertically Opposite Angles Definition

Vertically Opposite Angles are the angles opposite each other when 2 lines cross

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

a and c are vertically opposite angles. b and d are also vertically opposite angles.

Vertical Angles

The interesting thing here is that vertically opposite angles are equal:

a = c

b = d

(in fact they are congruent angles)

Example

Find angles a, b and c below:

Vertical Angles Example

Because b° is vertically opposite 60°, it must also be 60°

So, b = 60°

A full circle is 360°, so that leaves 360° − 2×60° = 240°

Angles a and c are also vertically opposite angles, so must be equal, which means they are 120° each.

Answer:

a = 120°, b = 60° and c = 120°.

Learn More

Exterior Angle Theorem

Supplementary Angles

Complementary Angles

Congruent Angles

Geometry Index

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