Question

what is ( mangle 1 )?
( mangle 1 = square^circ )

Explanation:

Step1: Find triangle's interior angle

First, calculate the unknown interior angle adjacent to $\angle 1$. The sum of interior angles in a triangle is $180^\circ$.
$180^\circ - 52^\circ - 86^\circ = 42^\circ$

Step2: Calculate $\angle 1$

$\angle 1$ and the $42^\circ$ angle are supplementary (form a straight line, sum to $180^\circ$).
$m\angle1 = 180^\circ - 42^\circ$

Answer:

$138^\circ$