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

(KS3, Year 8)

## 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°.## 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°.**Help Us To Improve Mathematics Monster**

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