GCSE Maths Practice: circle-theorems

Question 6 of 10

This question tests the property of opposite angles in a cyclic quadrilateral.

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\( \begin{array}{l}\text{What is true about opposite angles in a cyclic quadrilateral?}\end{array} \)

Choose one option:

\( \text{Add to } 180^\circ \) \( \text{Add to } 90^\circ \) \( \text{Add to } 270^\circ \) \( \text{Are equal} \)

Opposite angles in cyclic quadrilateral always sum to 180°.

In a cyclic quadrilateral (a four-sided figure with all vertices on a circle), the opposite angles always sum to 180°. This is a fundamental Circle Theorem. Knowing this allows students to calculate unknown angles, prove properties of cyclic quadrilaterals, and solve geometry problems involving inscribed figures. Practising this theorem improves diagram interpretation and reasoning skills for GCSE exams.