Question

Find the measure of a.
A. 60
B. 57
C. 40
D. 80

Answer 1

Option (C)

Explanation:

Since angle 'a' is the inscribed angle of the given triangle

Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.

x = 2a ⇒ a =
`(x)/(2)`

By the tangent-chord theorem,

"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"

`(x)/(2)` = 40°

Therefore, a =
`(x)/(2)` = 40°

Option (C) will be the answer.