Question

these figures are congruent. what is ( mangle q )?

Explanation:

Step1: Find $\angle V$ in $\triangle UVW$

The sum of angles in a triangle is $180^\circ$.
$$m\angle V = 180^\circ - 78^\circ - 60^\circ = 42^\circ$$

Step2: Match congruent triangle angles

$\triangle QSR \cong \triangle VUW$ (match sides: $QS=38$ corresponds to $VU=50$? No, match equal angles: $\angle S = \angle U = 78^\circ$, $\angle R = 42^\circ = \angle V$, so $\angle Q$ corresponds to $\angle W$).

Step3: Identify $m\angle Q$

Congruent triangles have matching equal angles, so $m\angle Q = m\angle W = 60^\circ$.

Answer:

$60$