Question

show that the measure of an exterior angle is always equal to the sum of the measures of its non - adjacent interior angles. use the figure below to help.
first identify the types of angles in the figure.
the exterior angle is ∠2. the non - adjacent interior angles are ∠1 and ∠3.
an exterior angle is outside the triangle.
non - adjacent angles are on the opposite side of the triangle from the exterior angle.

Explanation:

Step1: Recall angle definitions

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side, lying outside the triangle. Non - adjacent interior angles are the interior angles that are not adjacent (share a common side) with the exterior angle.
In the given triangle, $\angle2$ is outside the triangle, so it is the exterior angle. The interior angles not adjacent to $\angle2$ are $\angle1$ and $\angle3$ (since $\angle2$ is adjacent to the angle at the same vertex which is supplementary to it, and $\angle1$ and $\angle3$ are on the opposite side of the triangle from $\angle2$).

Step2: Verify the choices

For the exterior angle, from the options, $\angle2$ is the one outside the triangle, so it is the exterior angle. For non - adjacent interior angles, $\angle1$ and $\angle3$ are the ones not adjacent to $\angle2$.

Answer:

The exterior angle is $\boldsymbol{\angle2}$. The non - adjacent interior angles are $\boldsymbol{\angle1}$ and $\boldsymbol{\angle3}$.