Exercise 41 Page 787

Finding x

Let's pay close attention to the arcs whose measures are x^(∘) and 60^(∘).

An arc whose endpoints are the endpoints of a diameter has a measure of 180^(∘). Therefore, by the Arc Addition Postulate the sum of x and 60 is equal to 180. x + 60 = 180 ⇔ x = 120

Finding y

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

Therefore, y is half of 120. y=1/2(120) ⇔ y = 60 This corresponds to option D.