Question

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

Explanation:

Step1: Find third interior angle

First, calculate the unknown interior angle of the triangle using the fact that the sum of interior angles in a triangle is $180^\circ$.
$\text{Third interior angle} = 180^\circ - 32^\circ - 117^\circ = 31^\circ$

Step2: Calculate supplementary angle $\angle1$

Since $\angle1$ and the third interior angle are supplementary (they form a straight line, sum to $180^\circ$):
$m\angle1 = 180^\circ - 31^\circ$

Answer:

$149^\circ$