Q14 of 141 Page 420

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

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]


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