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Answer: So,. The sum of the measures of the angles of a quadrilateral is 360. Let m∠J = m∠K = x. ... CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 24. YZ.
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The measure of the angle XYZ in the given kite WXYZ is 45°
What is a kite?
A kite is a quadrilateral with reflection symmetry across a diagonal. Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides.
Given is a kite WXYZ, with angles 73° and 121°, sides WZ and WX are equal,
We are asked to find the measure of the angle XYZ
Since, WZ = WX
Therefore,
∠ WXY = ∠ WZY [properties of a kite]
∠ WXY = ∠ WZY = 121°
We now have measurements of three angles from the given kite,
Since, a kite is quadrilateral, and the sum of the interior angles of a quadrilateral is 360°
Therefore,
∠ WXY + ∠ WZY + ∠ XWZ + ∠ XYZ = 360°
121° + 121° + 73° + ∠ XYZ = 360°
∠ XYZ = 360° - 315°
∠ XYZ = 45°
Hence, the measure of the angle XYZ in the given kite WXYZ is 45°
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