Question

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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? the non - adjacent interior angles are? and?

Explanation:

Step1: Recall the definition of exterior angle

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. In the given figure, \(\angle4\) is formed by extending a side of the triangle, so \(\angle4\) is an exterior angle.

Step2: Recall the definition of non - adjacent interior angles

Non - adjacent interior angles to an exterior angle are the two interior angles of the triangle that do not share a vertex with the exterior angle. For exterior angle \(\angle4\), the non - adjacent interior angles are \(\angle1\) and \(\angle2\) (since \(\angle3\) is adjacent to \(\angle4\)).

Answer:

The exterior angle is \(\angle4\). The non - adjacent interior angles are \(\angle1\) and \(\angle2\).