Question

study the figure. what is the measure of the missing exterior angle, in degrees?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the third interior angle be $x$. So, $x + 53^{\circ}+53^{\circ}=180^{\circ}$.
$x=180^{\circ}-(53^{\circ}+ 53^{\circ})=180^{\circ}-106^{\circ}=74^{\circ}$.

Step2: Use the linear - pair property

The exterior angle and the adjacent interior angle of a triangle form a linear - pair (sum to 180°). Let the exterior angle be $y$.
If the adjacent interior angle is $74^{\circ}$, then $y + 74^{\circ}=180^{\circ}$.
$y=180^{\circ}-74^{\circ}=106^{\circ}$.
Another way:
The measure of an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
The two non - adjacent interior angles to the unknown exterior angle are $53^{\circ}$ and $53^{\circ}$.
So the exterior angle $=53^{\circ}+53^{\circ}=106^{\circ}$.

Answer:

$106$