Question

what values of w and x make $\triangle pqr \cong \triangle acb$?
(there are two right triangles, $\triangle pqr$ with right angle at q, side pq labeled $w + 39$, side pr labeled 43; $\triangle acb$ with right angle at c, side ab labeled $x + 35$, side ac labeled 90. also, there are input boxes for w and x.)

Explanation:

Step1: Match corresponding sides

Since $\triangle PQR \cong \triangle ACB$, corresponding sides are equal:

1. $PQ = AC$: $w + 39 = 50$
2. $PR = AB$: $43 = x + 35$

Step2: Solve for $w$

Isolate $w$ by subtracting 39:
$w = 50 - 39$

Step3: Solve for $x$

Isolate $x$ by subtracting 35:
$x = 43 - 35$

Answer:

$w = 11$
$x = 8$