Question

wxyz is a kite. angle wxy has a measure of 133 degrees and angle zyx has a measure of 34 degrees. find the measure of angle zwy

Explanation:

Step1: Recall kite - angle property

In a kite, the non - vertex angles are congruent and the sum of the interior angles of a quadrilateral is 360 degrees. Let $\angle ZWY = x$.

Step2: Use angle - sum formula for quadrilateral

We know that in kite $WXYZ$, $\angle WXY=133^{\circ}$, $\angle ZYX = 34^{\circ}$, and the two non - vertex angles at $W$ and $Z$ are equal. Let the measure of $\angle ZWY=\angle XWY$. The sum of the interior angles of a quadrilateral is $\angle WXY+\angle ZYX + 2\angle ZWY=360^{\circ}$.

Step3: Solve for $\angle ZWY$

Substitute the known values into the equation: $133 + 34+2x=360$. First, simplify the left - hand side: $167 + 2x=360$. Then, subtract 167 from both sides: $2x=360 - 167=193$. Divide both sides by 2: $x=\frac{193}{2}=96.5$.

Answer:

$96.5^{\circ}$