Chapter 8.3, Problem 65SPR

To determine

The angles measuring less than angle 11.

Answer to Problem 65SPR

  $m\angle 4,m\angle 9,m\angle 2,m\angle 6$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The measure of an exterior angle of a triangle is more than the measure of either of its corresponding remote interior angles.

In triangle CED, Corresponding remote interior angles of angle 11 are angle 4 and angle 9. Thus, exterior angle inequality shows that

  $\begin{array}{l}m\angle 4<m\angle 11\\ m\angle 9<m\angle 11\end{array}$

In triangle CEB, Corresponding remote interior angles of angle 4 are angle 2 and angle 6. Thus, exterior angle inequality shows that

  $\begin{array}{l}m\angle 2<m\angle 4\\ m\angle 6<m\angle 4\end{array}$

Therefore, the angles measuring less than angle 11 are:

  $m\angle 4,m\angle 9,m\angle 2,m\angle 6$