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I believe the answer is A.

With the inscribed angle theorem (?) we know that XWZ covers 186 degrees (2*93). Because XYZ covers the area opposite of XWZ, the measure is (360-186)/2 = 87.

B by itself does not give us this information since the angles overlap

Also this question feels like a 700 level. Either way it's a good one

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Bunuel

Quadrilateral WXYZ is inscribed in the circle above. What is the measure of angle XYZ?

(1) Angle XWZ measures 93 degrees.

(2) Angle YXW measures 106 degrees.

Attachment:
QuadrilateralWXYZ.png

In a cyclic Quadrilateral, sum of diagonally opposite angles = 180

Statement 1: XWZ=93
Then, XYZ= 180-93= 87
Sufficient

Statement 2: YXW= 106
This angle has no relation with XYZ hence
Not sufficient

Answer Option A
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Imo A
Cyclic quadrilateral have Opposite angle are supplementary

Angle xyz+angle xwz =180

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in a cycle quadrilateral sum of opposite sides is 180.

stat1: suff

stat2: not suff

ans A
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