Question

the diagonals of rectangle wxyz intersect at p. given that m yxz = 50° and xz = 16, find the indicated measure.

m∠wxp (just put the number)

Explanation:

Step1: Properties of rectangle diagonals

In a rectangle, diagonals are equal and bisect each other. So \( WX\parallel YZ\), and \(\angle WXZ=\angle YZX\) (alternate - interior angles). Also, \(\angle WXY = 90^{\circ}\).

Step2: Calculate \(\angle WXP\)

We know that \(\angle WXY=90^{\circ}\) and \(\angle YXZ = 50^{\circ}\).
Since \(\angle WXY=\angle WXP+\angle YXZ\) (angle - addition postulate).
Let \(m\angle WXP=x\). Then \(x + 50^{\circ}=90^{\circ}\).
Subtracting \(50^{\circ}\) from both sides gives \(x=90^{\circ}-50^{\circ}\).

Answer:

\(40\)