Question

Find the measure of the numbered angle.

Select one:

A. 62.5
B. 105
C. 112.5
D. 115

Answer 1

C. 112.5

Explanation:

The Angles of Intersecting Chords Theorem states:

"If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle"

So, the arc intercepted by the angle ∠5 is:

360° - 50° - 115° - 85° = 110°

On the other hand, the arc intercepted by its vertical angle is:

115°

Therefore:

`\angle 5 = (1)/(2)(110^(\circ)+115^(\circ)) \\ \\ \boxed{\angle 5 = 112.5^(\circ)}`