Question

In the figure, YX−→− and YZ−→− are tangents to circle A at points X and Z, respectively.

mXZ=140∘ mXSZ=220∘
What is the measure of ∠XYZ ?
Enter your answer in the box.

Answer 1

220 -140 = 80 / 2 = 40

Answer 2

The measure of ∠XYZ is 40°.

The measure of the central angle is equal to the measure of the minor arc. Since Arc XZ is the minor arc, central angle is equal to 140°.

∠XYZ = 1/2 (major arc - minor arc)
∠XYZ = 1/2 (220 - 140)
∠XYZ = 1/2 (80)
∠XYZ = 40°

I also solved the problem using the right triangles that are formed in the figure. Pls. see attachment