Chapter 7.1, Problem 63SPR

To determine

To list: The angles that satisfy the given condition.

Answer to Problem 63SPR

The angles with measures less than $m\angle 11$ are $\angle 4$ , $\angle 9$ , $\angle 2$ , and $\angle 6$ .

Explanation of Solution

Given:

The given condition is “measures less than $m\angle 11$ .”

Calculation:

Exterior Angle Inequality Theorem: An exterior angle of a triangle is greater than either of the non-adjacent interior angles.

Consider the following figure.

  

In $\Delta CED$ , $m\angle 11$ is a corresponding remote interior angles of and $\angle 9$ .

Thus, exterior angle inequality shows that $m\angle 4<m\angle 11$ and $m\angle 9<m\angle 11$ .

In $\Delta CEB$ , corresponding remote interior angle of $\angle 4$ are $\angle 2$ and $\angle 6$ .

Thus, exterior angle inequality shows that $m\angle 2<m\angle 4$ and $m\angle 6<m\angle 4$ .

Transitive Property of inequality shows that $m\angle 2<m\angle 11$ and $m\angle 6<m\angle 11$ .

Therefore, the angles with measures less than $m\angle 11$ are $\angle 4$ , $\angle 9$ , $\angle 2$ , and $\angle 6$ .