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 ?

Answer 1

The answer is 40!

Explanation:

Answer 2

We are given with
mXZ = 140∘
mXSZ = 220∘

and YX and YZ are tangents to circle A at X and Z.

According to the theorems on circles, the angles formed by the intersection of the two tangents is half the difference between of the measure of the arcs subtended by the tangents. So,
∠XYZ = (220 - 140) /2 = 40∘