Question

WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZWX has a measure of 34 degrees.

That means that angle ZWY has a measure of degrees and angle ZYW has a measure of degrees.

(Hint: Label the figure on page 235 to solve!).



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Answer 1

The measure of angle ZYW is 17 degrees and angle ZWY has a measure of 30 degrees

How to find the angle of the kite?

Statement 1: WX ≅ WZ; ZY ≅ XY; WY ≅ WY

Reason 1: Given

Statement 2: Triangles WXY & WZY are congruent

Reason 2: SSS Congruency Postulate

2. Now by CPCTC, all corresponding angles are Congruent.

Thus:

angle WZY ≅ Angle WXY = 133°

Sum of angles in a quadrilateral is 360 degrees. Thus:

angle WZY + Angle WXY + angle ZWX + angle ZYX = 360

angle ZWX = 360 - (133 + 133 + 34)

angle ZWX = 60°

Since Triangles WXY & WZY are congruent, then it means that:

angle ZYW ≅ angle XYW

angle ZWY ≅ angle XWY

Thus:

angle ZWY ≅ angle XWY

= 60/2 = 30°