Question

1. 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 sum of angles in a quadrilateral

The sum of the interior angles of a quadrilateral is 360 degrees. In kite WXYZ, we know two of the angles: $\angle WXY = 133^{\circ}$ and $\angle ZWX=60^{\circ}$.

Step2: Note property of angles in a kite

In a kite, the non - vertex angles are congruent. Let $\angle ZYW=\angle XYW = x$. So $\angle ZYX = 2x$.

Step3: Set up an equation

We have the equation $\angle WXY+\angle ZWX+\angle ZYX+\angle YZW=360^{\circ}$. Since $\angle YZW$ is not needed as we are focused on finding $\angle ZYW$ and we know $\angle ZYX = 2x$, substituting the known values gives $133 + 60+2x=360$.

Step4: Solve the equation

First, simplify the left - hand side: $193+2x = 360$. Then subtract 193 from both sides: $2x=360 - 193=167$. Divide both sides by 2: $x=\frac{167}{2}=83.5$.

Answer:

$83.5$