Question

what is m∠xyz? m∠xyz = (square^{circ})

Explanation:

Step1: Identify angle - bisector property

Since the two right - angled triangles share a common side \(YW\) and have equal hypotenuses (the red - marked equal segments), \(YW\) is the angle - bisector of \(\angle XYZ\).

Step2: Calculate \(\angle XYZ\)

If the measure of one of the two equal angles formed by the angle - bisector is \(36^{\circ}\), then \(m\angle XYZ = 2\times36^{\circ}\).

Answer:

\(72\)