Question

If the measure of a tangent-chord angle is 54 degrees, then what is the measure of the intercepted arc inside of the angle? a. 27, b. 108, c. 156, d. 54

Answer 1

When a tangent and a chord intersect at a point on a circle, the angle formed between the tangent and the chord is equal to half the measure of the intercepted arc inside the angle.

In this case, the measure of the tangent-chord angle is given as 54 degrees. Therefore, the measure of the intercepted arc inside the angle would be twice that, which is:

54 degrees * 2 = 108 degrees

Thus, the measure of the intercepted arc inside the angle is 108 degrees.

Therefore, the correct answer is b) 108.