Chapter 8.3, Problem 62SPR

To determine

The angles measuring less than angle 5.

Answer to Problem 62SPR

  $m\angle 2,<m\angle 10,m\angle 7,m\angle 8$

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 CBD, Corresponding remote interior angles of angle 5 are angle 2 and angle 10. Thus, exterior angle inequality shows that

  $\begin{array}{l}m\angle 2<m\angle 5\\ m\angle 10<m\angle 5\end{array}$

In triangle ABD, Corresponding remote interior angles of angle 10 are angle 8 and angle 7. Thus, exterior angle inequality shows that

  $\begin{array}{l}m\angle 7<m\angle 10\\ m\angle 8<m\angle 10\end{array}$

Therefore, the angles measuring less than angle 5 are:

  $m\angle 2,<m\angle 10,m\angle 7,m\angle 8$