Circle Theorem: Opposite Angles in a Cyclic Quadrilateral Add Up to 180°
(KS3, Year 8)
The LessonA cyclic quadrilateral is a 4 sided shape where each corner touches the circle. Both pairs of opposite angles add up to 180°.
Lesson SlidesThe slider below shows why opposite angles in a cyclic quadrilateral add up to 180°. Open the slider in a new tab
How to Use the Circle Theorem where Opposite Angles in a Cyclic Quadrilateral Add Up to 180°
QuestionWhat is the angle θ in the circle below?
The opposite angles add up to 180°.
70° + θ = 180°
Subtract the known angle from 180°.
θ = 180° − 70° = 110°
Answer:The angle θ is 110°.
- Do you disagree with something on this page?
- Did you spot a typo?