Answer:
m∠QPR = 35° m∠QPM =40° m∠PRS = 30°
Step-by-step explanation:
ΔPRQ is a right triangle with right angle at R. So m∠QPR = 90 - 55 = 35
ΔQPM is a right triangle with right angle at M. So m∠QPM = 90 - 40 = 40
Arc RQ = 2(35) = 70 and arc SR = 2(25) = 50.
So arc PS = 180 - (arc RQ + arc SR) = 180 - (70 + 50) = 180 - 120 = 60
Now arc PS is the intercepted arc for ∠PRS.
Therefore, m∠PRS = 60/2 = 30
I used the fact that an inscribed angle has a measure 1/2 the measure of the intercepted arc several times. Also, I used the fact that the acute angles of a right triangle are complementary. And, finally I used the fact that an inscribed angle in a semicircle is a right angle.
I hope this helped.
