Exercise 40 Page 787

Finding y

Pay close attention to the arcs whose measures are y^(∘) and 130^(∘).

An arc whose endpoints are the endpoints of a diameter has a measure of 180^(∘). Therefore, by the Arc Addition Postulate the sum of y and 130 is equal to 180. y + 130 = 180 ⇔ y = 50

Finding x

The Inscribed Angle Theorem says that the measure of an inscribed angle is half the measure of its intercepted arc.

Therefore, x is half of 50. x=1/2(50) ⇔ x = 25 This corresponds to option A.