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 sum property

The sum of the interior angles of a quadrilateral is 360 degrees. In a kite, one pair of opposite angles are equal.

Step2: Let \(\angle ZYW = \angle XYW=\theta\), so \(\angle ZYX = 2\theta\)

We know \(\angle WXY=133^{\circ}\) and \(\angle ZWX = 60^{\circ}\)

Step3: Apply the angle - sum formula for a quadrilateral

\(\angle ZWX+\angle WXY+\angle ZYX+\angle YZW=360^{\circ}\)
Since \(\angle ZYX = 2\theta\), we have \(60 + 133+2\theta+\angle YZW=360\)
In a kite, the non - congruent angles are supplementary to the sum of the other two angles. But we can also directly use the angle - sum formula.
\(2\theta=360-(133 + 60)\)
\(2\theta=360 - 193\)
\(2\theta = 167\)
\(\theta=\frac{167}{2}=83.5\)
So \(\angle ZYW = 83.5\) degrees

Answer:

83.5