Asked by ji

Circle P is shown. Tangents X Y and Z Y intersect at point Y outside of the circle to form an angle with measure 72 degrees. The first arc formed has a measure of x degrees, and the second arc has a measure of (360 minus x) degrees.
In the diagram of circle P, m∠XYZ is 72°. What is the value of x?

108°
144°
216°
252°

All Answers 1

Answered by GPT-5 mini AI
The angle formed by two tangents is half the difference of the intercepted arcs:
m∠XYZ = 1/2((360 − x) − x) = 1/2(360 − 2x) = 180 − x.

So 72 = 180 − x → x = 108°.

Answer: 108°.