Question

triangle jlk: ∠j = 58°, ∠l = 79°, ∠k = 43°, jl = 40 mm, lk = 50 mm
triangle wyx: ∠w = 79°, xy = 58 mm
these figures are congruent. what is wx?
$square$ millimeters

Explanation:

Step1: Match congruent triangle parts

First, identify corresponding angles: In $\triangle JLK$, $\angle L = 79^\circ$, which matches $\angle W = 79^\circ$ in $\triangle WYX$.
Corresponding sides: Side opposite $\angle K (43^\circ)$ in $\triangle JLK$ is $JL = 40$ mm. In $\triangle WYX$, the side opposite the corresponding angle (which will be equal to $43^\circ$) is $XY = 58$ mm? No, correct correspondence: $\triangle JLK \cong \triangle WYX$ (matching angles: $\angle L = \angle W = 79^\circ$, $\angle J = \angle Y = 58^\circ$, so $\angle K = \angle X = 43^\circ$).
So side $WX$ corresponds to side $LK$.

Step2: State congruent side length

Since congruent triangles have equal corresponding sides, $WX = LK$.
$LK = 50$ mm, so $WX = 50$ mm.

Answer:

50 millimeters