Question

if wz = yz = 12 and m∠wxz = 52°, what is m∠wxy?
m∠wxy = \boxed{\circ}

Explanation:

Step1: Analyze Triangle WXZ and YXZ

In triangles \( \triangle WXZ \) and \( \triangle YXZ \), \( WZ = YZ = 12 \), \( \angle XWZ=\angle XYZ = 90^\circ \) (right angles), and \( XZ \) is common. So, \( \triangle WXZ \cong \triangle YXZ \) (HL congruence). Thus, \( \angle WXZ=\angle YXZ = 52^\circ \).

Step2: Calculate \( \angle WXY \)

\( \angle WXY=\angle WXZ+\angle YXZ \). Substituting the values, we get \( \angle WXY = 52^\circ+52^\circ = 104^\circ \).

Answer:

\( 104 \)