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Circle Theorem: Opposite Angles in a Cyclic Quadrilateral Add Up to 180° (Mathematics Lesson)

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

Step 2: Subtract the known angle from 180°.
θ = 180° - 70° = 110°

The angle θ is 110°.

A Real Example of How to Use the Circle Theorem that Opposite Angles in a Cyclic Quadrilateral Add Up to 180°

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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Note
WHAT IS A CIRCLE?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

CIRCLE THEOREMS

Circle theorems relate to the angles and lines within circles.

That opposite angles in a cyclic quadrilateral add up to 180° is one of the circle theorems. There are several others.

Read more about circle theorems