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# Circle Theorem: Angles in the Same Segment Are Equal

(KS3, Year 8)

## The Lesson

All triangles drawn from a chord in a circle make the same angle at the circumference.## How to Use the Circle Theorem where the Angles in the Same Segment Are Equal

## Question

What is the angle θ in the circle below?## Step-by-Step:

# 1

The angles subtended by the chord at the circumference of the circle are equal.

θ = 40°

## Answer:

The angle θ is 40°.## Useful Definitions

A semicircle is half a circle. A**chord**is a line whose endpoints lie on the circle.

A

**segment**is a region, not containing the center, bounded by a chord and an arc lying between the chord's endpoints.

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