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°.

Why Do the Opposite Angles in a Cyclic Quadrilateral Add Up to 180°?

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

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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°.

Slider

The slider below shows a real example of the circle theorem that opposite angles in a cyclic quadrilateral add up to 180°.

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See Also

What is a circle? What are the circle theorems?