The Lesson

A cyclic quadrilateral is a 4 sided shape where each corner touches the circle. Both pairs of opposite angles add up to 180°.

Lesson Slides

The slider below shows why opposite angles in a cyclic quadrilateral add up to 180°.

How to Use the Circle Theorem where Opposite Angles in a Cyclic Quadrilateral Add Up to 180°

Question

What is the angle θ in the circle below?

Step-by-Step:

1

The opposite angles add up to 180°.
70° + θ = 180°

2

Subtract the known angle from 180°.
θ = 180° − 70° = 110°

Answer:

The angle θ is 110°.