Question

these figures are congruent. what is $m\angle v$? $\square^\circ$

Explanation:

Step1: Find $\angle F$ in $\triangle EGF$

The sum of angles in a triangle is $180^\circ$.
$\angle F = 180^\circ - 62^\circ - 79^\circ = 39^\circ$

Step2: Match congruent triangle parts

$\triangle EGF \cong \triangle XVW$: $EG=32$ (corresponds to $XV$), $EF=50$ (corresponds to $VW=50$), $\angle F=39^\circ$ (corresponds to $\angle W=39^\circ$). So $\angle V$ corresponds to $\angle G$.

Step3: Identify $m\angle V$

Congruent triangles have congruent corresponding angles, so $m\angle V = m\angle G$.

Answer:

$79^\circ$