Question

for the figure shown, find m∠1 and m∠2. m∠1 = 127°. m∠2 = □° (the figure is not drawn to scale.)

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the triangle with $\angle1$ as an exterior angle, if the two non - adjacent interior angles are $32^{\circ}$ and another angle (let's call it $x$). But we are directly given $m\angle1 = 127^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. A linear pair of angles is supplementary, meaning the sum of the measures of two angles in a linear pair is $180^{\circ}$. So, $m\angle1+m\angle2 = 180^{\circ}$.
We know $m\angle1 = 127^{\circ}$, then $m\angle2=180^{\circ}-m\angle1$.
$m\angle2 = 180 - 127$

Answer:

$53$