Question

wxyz is a kite. angle wxy has a measure of 133° and angle zyx has a measure of 34°.
find the measure of angle zwy.
type your answer in the box.
angle zwy has a measure of

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\).

Step2: Use the properties of a kite

In a kite \(WXYZ\) with \(WZ = WX\) and \(ZY=XY\), \(\angle WZY=\angle WXY = 133^{\circ}\) (the non - vertex angles are equal). Let \(\angle ZWY=\angle XWY=\alpha\).
We know that \(\angle ZYX = 34^{\circ}\).
By the angle - sum formula for quadrilaterals: \(\angle WZY+\angle ZYX+\angle WXY+\angle WZY = 360^{\circ}\). Substituting the known values: \(133^{\circ}+34^{\circ}+133^{\circ}+2\alpha=360^{\circ}\).
First, simplify the left - hand side: \(300^{\circ}+2\alpha=360^{\circ}\).
Then, solve for \(\alpha\): \(2\alpha=360^{\circ}- 300^{\circ}=60^{\circ}\), so \(\alpha = 30^{\circ}\).

Answer:

\(30^{\circ}\)