Question

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

Explanation:

Step1: Match congruent triangle parts

In $\triangle SRQ$ and $\triangle VWX$, side $SR=50\ \text{cm}$ matches side $VW=50\ \text{cm}$, $\angle S=58^\circ$ matches $\angle X=58^\circ$. So $\angle R$ corresponds to $\angle W$.

Step2: Identify $\angle W$ measure

$\angle W$ is a right angle, so $m\angle W=90^\circ$.

Step3: Equate corresponding angles

Since congruent triangles have equal corresponding angles, $m\angle R=m\angle W$.

Answer:

$90$