Question

1. find m∠lmn. l (4x + 2)° m (7x - 37)° n p

Explanation:

Step1: Set up an equation

Since the sum of angles in a triangle formed by the angles at $M$ and the right - angled corners in the figure (assuming it's a relevant geometric shape with some angle - related properties), we know that the two non - right angles at $M$ are equal. So we set up the equation $4x + 2=7x-37$.
$4x + 2=7x-37$

Step2: Solve for $x$

First, move the $x$ terms to one side and the constants to the other side. Subtract $4x$ from both sides:
$2 = 7x-4x-37$
$2=3x - 37$.
Then add 37 to both sides:
$2 + 37=3x$
$39 = 3x$.
Divide both sides by 3:
$x=\frac{39}{3}=13$.

Step3: Find $m\angle LMN$

We can use either of the angle expressions. Let's use $4x + 2$. Substitute $x = 13$ into it:
$m\angle LMN=4x + 2=4\times13+2=52 + 2=54^{\circ}$.

Answer:

$54^{\circ}$