Question

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

Explanation:

Step1: Find adjacent interior angle

The 146° angle and its adjacent interior angle form a linear pair, so they add to 180°.
$\text{Adjacent interior angle} = 180^\circ - 146^\circ = 34^\circ$

Step2: Calculate $m\angle1$

The sum of angles in a triangle is 180°. Use the known angles to solve for $\angle1$.
$m\angle1 = 180^\circ - 64^\circ - 34^\circ$

Answer:

$82$