Question

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

Explanation:

Step1: Match congruent triangle parts

First, identify corresponding parts: In $\triangle STU$, $\angle S=45^\circ$, $\angle U=60^\circ$, $\angle T=75^\circ$. Side $SU=56$ yd, $ST=50$ yd. In $\triangle YXW$, side $YX=41$ yd, $\angle Y=60^\circ$. Since triangles are congruent, $\angle Y$ corresponds to $\angle U$ (both $60^\circ$), so $\angle X$ corresponds to $\angle T$.

Step2: Confirm corresponding angle measure

Corresponding angles in congruent triangles are equal, so $m\angle X = m\angle T$.

Answer:

$75$