Question

1. use the figure shown to answer each question.

a. explain how you can use the exterior angle theorem to calculate the measure of ∠pmu.
b. calculate the measure of ∠pmu.

Explanation:

Step1: Recall exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.

Step2: Identify non - adjacent interior angles

In the triangle with exterior angle $\angle PMU$, the non - adjacent interior angles to $\angle PMU$ are the $21^{\circ}$ and $35^{\circ}$ angles.

Step3: Calculate the measure of $\angle PMU$

$\angle PMU=21^{\circ}+35^{\circ}=56^{\circ}$

Answer:

$56^{\circ}$