Question

the measure of the exterior angle equals
the sum of the measures of the
non - adjacent interior angles.
what is m∠5?
m∠5 = 110°
does m∠5 equal the sum of the measures
of its non - adjacent interior angles? explain.
yes, because 50°+60° = 110°.
no, because 70°+50°≠110°.
no, because 70°+60°≠110°.
(there is a triangle with angles 50°, 70°, 60° and exterior angles 120° and the angle at position 5)

Explanation:

Step1: Identify non - adjacent angles

The non - adjacent interior angles to $\angle5$ in the triangle are the angles with measures $50^{\circ}$ and $60^{\circ}$, since the adjacent interior angle to $\angle5$ is $70^{\circ}$.

Step2: Calculate the sum of non - adjacent angles

Calculate the sum of the non - adjacent interior angles: $50^{\circ}+60^{\circ}=110^{\circ}$.

Step3: Compare with $m\angle5$

We know that $m\angle5 = 110^{\circ}$. So, the sum of the measures of the non - adjacent interior angles is equal to $m\angle5$.

Answer:

Yes, because $50^{\circ}+60^{\circ}=110^{\circ}$.