Chapter 5.3, Problem 11PPS

To determine

To list: The angles that measures lessthan $m\angle 9$ .

Answer to Problem 11PPS

The angle that measures less than $m\angle 9$ is $\angle 1,\angle 3,\angle 6,\angle 7$ .

Explanation of Solution

The $\angle 9$ is an exterior angle of the triangle with $\angle 6,\angle 7,\angle 8$ . Angles $\angle 6$ and $\angle 7$ are the corresponding remote interior angles. By the exterior angle inequality theorem, the measure of $\angle 9$ is greater than the measure of $\angle 6$ and the measure of $\angle 9$ is greater than the measure of $\angle 7$

Also, $\angle 9$ is an exterior angle the largest triangle. $\angle 1,\angle 3,\angle 6$ are the corresponding remote interior angles. By the exterior angle inequality theorem, the measure of $\angle 9$ is greater than the measure of $\angle 1,\angle \text{3,}\angle \text{6}$ .

Therefore, the angle that measures less than $m\angle 9$ is $\angle 1,\angle 3,\angle 6,\angle 7$ .