Question

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:

\(60\)