Question

1. determine the measure of the unknown angle in each triangle. a) b.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Calculate the unknown angle in triangle ABC

Let the unknown angle be $\angle B$. We know that $\angle A = 78^{\circ}$ and $\angle C=37^{\circ}$. Using the angle - sum property $\angle A+\angle B+\angle C = 180^{\circ}$. So, $\angle B=180^{\circ}-\angle A - \angle C=180^{\circ}-78^{\circ}-37^{\circ}=65^{\circ}$.

Step3: Calculate the unknown angle in triangle PQR

Let the unknown angle be $\angle R$. We know that $\angle P = 80^{\circ}$ and $\angle Q = 66^{\circ}$. Using the angle - sum property $\angle P+\angle Q+\angle R=180^{\circ}$. So, $\angle R=180^{\circ}-\angle P-\angle Q=180^{\circ}-80^{\circ}-66^{\circ}=34^{\circ}$.

Answer:

a. The measure of $\angle B$ is $65^{\circ}$.
b. The measure of $\angle R$ is $34^{\circ}$.