Chord of a circle subtends angles at two points and on the same segment

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

Chord

PQ

of a circle subtends angles at two points

R

and

S

on the same segment. It is given that

\angle PRQ = 40^\circ

and

\angle QPS = 64^\circ

. Answer the following. (i) Calculate

\angle PSQ

. (ii) Find

\angle PQS

. (iii) Determine the three interior angles of

\triangle PQS

and verify that their sum is

180^\circ