Question

question 6
if quadrilateral defg - quadrilateral wxyz, find m∠w
note: figures are not to scale.

Explanation:

Step1: Recall the property of similar quadrilaterals

Similar quadrilaterals have corresponding angles equal. The sum of interior angles of a quadrilateral is \(360^{\circ}\).

Step2: Calculate the measure of \(\angle D\)

Let \(m\angle D=x\). Using the angle - sum formula for quadrilaterals \(x + 57^{\circ}+85^{\circ}+87^{\circ}=360^{\circ}\).

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Since quadrilateral \(DEFG\sim\) quadrilateral \(WXYZ\), \(\angle D\) and \(\angle W\) are corresponding angles.

Answer:

\(131^{\circ}\)