Question

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

Explanation:

Step1: Match congruent triangle parts

In $\triangle LMK$ and $\triangle SQR$, $\angle L = \angle S = 43^\circ$. Side $LK=63$ mi corresponds to side $QR=50$ mi? No, match by angle-side: $\angle L$ is between $LM$ and $LK$; $\angle S$ is between $SQ$ and $SR$. So $\triangle LMK \cong \triangle SQR$ where $\angle K$ corresponds to $\angle R$.

Step2: Identify corresponding angle measure

In $\triangle LMK$, $m\angle K = 79^\circ$. Congruent triangles have congruent corresponding angles.

Answer:

$79^\circ$