Question

what is wz? wz =

Explanation:

Step1: Identify congruent triangles

In right - triangles $\triangle YXZ$ and $\triangle WXZ$, $\angle YXZ=\angle WXZ = 43^{\circ}$, $\angle YZX=\angle WZX$ (common angle), and $\angle ZYX=\angle ZWX = 90^{\circ}$. Also, $XZ$ is common to both triangles. So, $\triangle YXZ\cong\triangle WXZ$ by the Angle - Angle - Side (AAS) congruence criterion.

Step2: Use congruence property

Since $\triangle YXZ\cong\triangle WXZ$, corresponding sides are equal. Given $YZ = 46$, and $YZ$ and $WZ$ are corresponding sides in the congruent triangles. So, $WZ=YZ$.

Answer:

$46$