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

Explanation:

Step1: Find the interior angle adjacent to ∠1

First, calculate the unknown interior angle of the triangle using the fact that the sum of interior angles in a triangle is $180^\circ$. $180^\circ - 83^\circ - 31^\circ = 66^\circ$

Step2: Calculate m∠1

∠1 and the 66° angle are supplementary (they form a linear pair, summing to $180^\circ$). $m\angle1 = 180^\circ - 66^\circ$

Answer:

$114^\circ$