Find the measure of the arc or angle indicated. Provide a perfect solution.
Given: Arc MK = 116, Angle K = 47
Need: Arc KL
Choices:
A) 77
B) 167
C) 109
D) 150
The answer is D) 150. Please explain why
The measure of an arc is equal to the measure of its intercepted angle. Since Arc MK = 116 and Angle K = 47, the measure of Arc KL must be 116 - 47 = 69. Since Arc KL is part of a circle, it must be a full angle, so the measure of Arc KL must be 360 - 69 = 150.
TRUE ANSWER:
47° x 2 = 94° (The measurement of the central angle is twice that of the inscribed angle)
116° + 94° = 210°
360° - 210° = 150°