Question

in triangle lmn: side lm is $2x+11$, angle at m is $(y+10)^{circ}$
in triangle qrs: side rq is $3x - 9$, angle at r is $(2y-40)^{circ}$
$x =$ type your answer...
$y =$ type your answer...

Explanation:

Step1: Set equal congruent angles

The marked angles $\angle M$ and $\angle R$ are congruent, so:
$y + 10 = 2y - 40$

Step2: Solve for $y$

Rearrange to isolate $y$:
$10 + 40 = 2y - y$
$y = 50$

Step3: Set equal congruent sides

The marked sides $LM$ and $QR$ are congruent, so:
$2x + 11 = 3x - 9$

Step4: Solve for $x$

Rearrange to isolate $x$:
$11 + 9 = 3x - 2x$
$x = 20$

Answer:

$x = 20$
$y = 50$