# 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°:##### Curriculum

##### Interactive Test

**show**

##### 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