Mathematics

Problem

In quadrilateral

PQRS

the following measurements are known:

\angle PQR = 70^\circ

\angle PSR = 70^\circ

and

\angle QPR = 38^\circ

. a. (i) Prove that the four points

P,\,Q,\,R

and

S

are concyclic. b. (ii) Calculate

\angle PRQ

. c. (iii) Determine

\angle PSQ

. State clearly every theorem or property you use in each step.