Question

what is m∠r? these figures are congruent. what is m∠r?

Explanation:

Step1: Recall congruent - triangle property

Corresponding angles of congruent triangles are equal.

Step2: Identify corresponding angles

Since the two triangles are congruent, $\angle R$ corresponds to $\angle L$.

Step3: Calculate $\angle L$ in $\triangle LMN$

In right - triangle $LMN$, $\angle M = 90^{\circ}$, $\angle N=56^{\circ}$. Using the angle - sum property of a triangle ($\angle L+\angle M+\angle N = 180^{\circ}$), we have $\angle L=180^{\circ}-\angle M - \angle N=180^{\circ}-90^{\circ}-56^{\circ}=34^{\circ}$.

Step4: Find $\angle R$

Since $\angle R=\angle L$, $m\angle R = 34^{\circ}$.

Answer:

$34$