Question

these figures are congruent. what is m∠q?

Explanation:

Step1: Recall triangle congruence

Congruent triangles have corresponding angles equal. So we can find the measure of angle \( Q \) by using the fact that the sum of angles in a triangle is \( 180^\circ \), or by identifying corresponding angles from the congruent triangles.

Step2: Calculate angle in first triangle

In triangle \( PQR \), we know two angles: \( \angle R = 63^\circ \), \( \angle P = 38^\circ \). The sum of angles in a triangle is \( 180^\circ \), so \( \angle Q=180^\circ - 63^\circ - 38^\circ \).
Calculating: \( 180 - 63 - 38 = 79^\circ \). Alternatively, by congruence, we can match the sides and angles. The second triangle has angles \( 79^\circ \) and \( 38^\circ \), and since they are congruent, the corresponding angle to \( \angle Q \) can be found by angle - sum or correspondence.

Answer:

\( 79^\circ \)