Question

What is the measure of XYZ?

Answer 1

Answer:

Option B. 72°

Step-by-step explanation:

Two chords WX and VZ intersect each other at a point Y.

mArc VX = 64°

mArc WZ = 152°

As we know angle ∠ VYX formed by two intersecting chords inside the circle can be measure by

m∠VYX = $\frac{1}{2}(mVX + mWZ)=\frac{1}{2}(64+152)=\frac{216}{2}=108$

Since ∠VYX and ∠XYZ are supplementary angles.

So ∠VYX + ∠XYZ = 180

108 + ∠XYZ = 180

∠XYZ = 180 - 108 = 72°

Option B. 72° is the answer.

Answer 2

B    72

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