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 diagram, if we consider the angles around point Q, we know that \(\angle PQR+\angle SQR = 180^{\circ}\) (a straight - angle).

Step2: Solve for \(\angle PQR\)

Given \(\angle SQR = 20^{\circ}\), and using the equation \(\angle PQR+\angle SQR=180^{\circ}\), we can substitute the value of \(\angle SQR\) into the equation: \(\angle PQR=180^{\circ}-\angle SQR\). So, \(\angle PQR = 180 - 20=160^{\circ}\). The postulate used to find the measure of \(\angle PQR\) based on the relationship between adjacent angles is the angle - addition postulate.

Answer:

angle addition postulate