# Circle Theorem: Opposite Angles in a Cyclic Quadrilateral Add Up to 180°

## Circle Theorem: Opposite Angles in a Cyclic Quadrilateral Add Up to 180°

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

## How to Use the Circle Theorem that 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°.