Vertical Angles

Definition

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

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

Example

Vertical Angles

a° and b° are vertical angles.

Vertical Angles are Congruent Angles

The interesting thing here is that vertical angles are congruent angles:

a° = b°

they are equal

Example

Find angles a°, b° and c° below:

Vertical Angles Example

Because a° is vertically opposite 100°, it must also be 100°

A full circle is 360°, so that leaves 360° − 2×100° = 160°

Angles b° and c° are also vertical angles, so must be equal, which means they are 80° each.

Answer: a = 100°, b = 80° and c = 80°.

Learn More

Finding an Angle in a Right Angled Triangle

Angles of Elevation & Depression

Consecutive Interior Angles

Lines of Symmetry of Plane Shapes

Geometry Index

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