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.

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