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

Explanation:

Step1: Recall triangle angle - sum property

The sum of interior angles of a triangle is (180^{\circ}).

Step2: Identify corresponding angles

Since the triangles are congruent, (\angle G) corresponds to (\angle R).

Step3: Calculate (m\angle R)

We know that in (\triangle FHG), (m\angle H = 77^{\circ}), (m\angle G=60^{\circ}). Using the angle - sum property (m\angle F=180^{\circ}-(77^{\circ} + 60^{\circ})=43^{\circ}). But more directly, because of congruence, (m\angle R=m\angle G) (by the property of congruent triangles: corresponding angles are equal).

Answer:

(60)