Question

1. which postulate explains why angle pqr would be 140 degrees in the picture below? angle addition postulate addition postulate sum angle postulate interior angles postulate

Explanation:

Step1: Recall angle - addition postulate

The angle - addition postulate states that if we have two adjacent angles, the measure of the larger angle formed is the sum of the measures of the two smaller adjacent angles. In the given figure, if we consider the large angle $\angle PQR$ and the two adjacent angles $\angle PQS$ and $\angle SQR$.

Step2: Analyze the given angles

We know that $\angle PQS = 160^{\circ}$ and $\angle SQR=20^{\circ}$. By the angle - addition postulate, $\angle PQR=\angle PQS-\angle SQR$. Substituting the values, we get $\angle PQR = 160^{\circ}- 20^{\circ}=140^{\circ}$.

Answer:

angle addition postulate