Question

wxyz is a kite. angle wxy has a measure of 133 degrees and angle zwx has a measure of 60 degrees. find the measure of angle zyw. angle zyw has a measure of ____ degrees.

Explanation:

Step1: Recall kite - angle property

In a kite, one pair of opposite angles are equal. Also, the sum of the interior angles of a quadrilateral is 360 degrees. Let \(\angle WXY = 133^{\circ}\) and \(\angle ZWX=60^{\circ}\). Let \(\angle ZYW = \angle ZXW\).

Step2: Use angle - sum formula for quadrilateral

We know that for quadrilateral \(WXYZ\), \(\angle WXY+\angle ZWX+\angle XYZ+\angle YZW = 360^{\circ}\). In a kite, the non - congruent angles are \(\angle WXY\) and \(\angle YZW\), and the congruent angles are \(\angle ZWX\) and \(\angle ZYX\).
Let's assume the measure of \(\angle ZYW=x\).
We know that \(\angle ZWX = 60^{\circ}\), \(\angle WXY=133^{\circ}\).
Since the sum of the interior angles of a quadrilateral is 360 degrees, we have \(133 + 60+2x=360\).

Step3: Solve the equation for \(x\)

First, simplify the left - hand side of the equation: \(193 + 2x=360\).
Subtract 193 from both sides: \(2x=360 - 193\).
\(2x = 167\).
Divide both sides by 2: \(x=\frac{167}{2}=83.5\).

Answer:

83.5