Question

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

Explanation:

Step1: Find adjacent interior angle

The 117° angle is supplementary to the interior angle of the triangle next to it.
$180^\circ - 117^\circ = 63^\circ$

Step2: Calculate $\boldsymbol{m\angle1}$

Use the triangle angle sum theorem (sum of interior angles = 180°).
$m\angle1 = 180^\circ - 49^\circ - 63^\circ$

Answer:

$68^\circ$