In the given figure, is a diameter of a circle with center If and find and

Question

Philoid · Accepted Answer

In triangle PQR,

∠QPR + ∠PQR + ∠PRQ = 180°[Sum of angles of triangle]

⇒ ∠QPR + 65° + 90° = 180°

⇒ ∠QPR + 155° = 180°

⇒ ∠QPR = 25°______________ (i)

In triangle PMQ,

∠QPM + ∠PMQ + ∠PQM = 180°[Sum of angles of triangle]

⇒ ∠QPM + 90° + 50° = 180°

⇒ ∠QPM + 140° = 180°

⇒ ∠QPM = 40°

Now,

∠PRS = ∠QPR = 25°[Alternate angles]