Angles in Cyclic Quadrilaterals (Cambridge (CIE) IGCSE International Maths)

Cyclic Quadrilaterals

Circle theorem: Opposite angles in a cyclic quadrilateral add up to 180°

• A quadrilateral that is formed by four points on the circumference of a circle, (a cyclic quadrilateral), will have pairs of opposite angles that add up to 180°

• To spot this theorem in a diagram

  • look for quadrilaterals that have all four points on the circumference

• When explaining this theorem in an exam you must use the keywords: 

  • Opposite angles in a cyclic quadrilateral add up to 180°

• The theorem only works for cyclic quadrilaterals

  • The diagram below shows a common scenario that is not a cyclic quadrilateral