In a circle with centre

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

O

, chords

PQ

and

RS

are equal. They subtend angles at the centre such that

\angle POQ = (7x - 3)^\circ \quad \text{and} \quad \angle ROS = (5x + 17)^\circ.

Answer the following. (i) Find the value of

x

. (ii) Hence find the numerical measures of

\angle POQ

and

\angle ROS

. Explain each step of your working.