Question

these figures are congruent. what is wx? meters submit

Explanation:

Step1: Find missing angle in $\triangle JLK$

Sum of angles in triangle is $180^\circ$.
$\angle K = 180^\circ - 78^\circ - \angle J$
First calculate $\angle X$ in $\triangle WXY$: $\angle X = 180^\circ - 43^\circ - 59^\circ = 78^\circ$
Since triangles are congruent, $\angle L = \angle X = 78^\circ$, $LK = XY = 50\ \text{m}$. So $\angle K = \angle Y = 59^\circ$, $\angle J = \angle W = 43^\circ$.

Step2: Match congruent sides

Corresponding sides of congruent triangles are equal. Side $WX$ corresponds to side $JK$, and side $JK$ corresponds to side $JL$'s pair? No, correct match: $\triangle JLK \cong \triangle XWY$ (by angle-side-angle: $\angle L=\angle X=78^\circ$, $LK=XY=50\ \text{m}$, $\angle K=\angle Y=59^\circ$). So $WX = JK$? No, wait: $\angle J = \angle W=43^\circ$, $\angle L=\angle X=78^\circ$, $\angle K=\angle Y=59^\circ$, so sides: $JL = WX$, $LK = XY$, $JK = WY$.
$JL = 63\ \text{m}$, so $WX = JL$.

Answer:

63 meters