Question

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

Explanation:

Step1: Find adjacent interior angle

The 109° angle is supplementary to its adjacent interior angle of the triangle.
$180^\circ - 109^\circ = 71^\circ$

Step2: Sum triangle interior angles

The sum of interior angles of a triangle is $180^\circ$. Let $m\angle1 = x$.
$x + 71^\circ + 57^\circ = 180^\circ$

Step3: Solve for $m\angle1$

Calculate the sum of known angles, then subtract from $180^\circ$.
$x = 180^\circ - (71^\circ + 57^\circ) = 180^\circ - 128^\circ = 52^\circ$

Answer:

$52$