Question

what is $m\angle 1$?
diagram of a triangle with an exterior angle of 148° and an interior angle of 113°, angle 1 is to be found
$m\angle 1 = \square^\circ$

Explanation:

Step1: Find adjacent interior angle

The 148° angle is supplementary to its adjacent interior angle of the polygon.
$180^\circ - 148^\circ = 32^\circ$

Step2: Use triangle angle sum property

The polygon is a triangle, so the sum of interior angles is $180^\circ$. Let $m\angle 1 = x$.
$x + 113^\circ + 32^\circ = 180^\circ$

Step3: Solve for $x$

Calculate the sum of known angles, then subtract from $180^\circ$.
$x = 180^\circ - (113^\circ + 32^\circ) = 180^\circ - 145^\circ = 35^\circ$

Answer:

$35$