Chapter 8.3, Problem 63SPR

To determine

The angles measuring more than angle 6.

Answer to Problem 63SPR

  $m\angle 4,<m\angle 1,m\angle 11$

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 CEB, Corresponding remote interior angles of angle 4 is angle 6. Thus, exterior angle inequality shows that

  $m\angle 6<m\angle 4$

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

  $m\angle 4<m\angle 11$

In triangle CBD, Corresponding remote interior angles of angle 1 is sum of angle 6 and 9. Thus, exterior angle inequality shows that

  $m\angle 6+m\angle 9<m\angle 1$

Therefore, the angles measuring more than angle 6 are:

  $m\angle 4,<m\angle 1,m\angle 11$