Chapter 7.1, Problem 61SPR

To determine

To list: The angles that satisfy the given condition.

Answer to Problem 61SPR

The angles with measures greater than $m\angle 6$ are $\angle 4,\angle 1$ , and $\angle 11$ .

Explanation of Solution

Given:

The given condition is “measures greater than $m\angle 6$ .”

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 $\Delta CEB$ , $\angle 6$ is a corresponding remote interior angles of $\angle 4$ .

Thus, exterior angle inequality shows that $m\angle 4>m\angle 6$ .

In $\Delta CED$ , $\angle 4$ is a corresponding remote interior angle of $\angle 11$ .

Thus, exterior angle inequality shows that $m\angle 11>m\angle 4$ .

In $\Delta CBD$ , $\angle 6+\angle 9$ is a corresponding remote interior angle of $\angle 1$ .

Thus, exterior angle inequality shows that $m\angle 1>m\angle 6+m\angle 9$ .

Transitive property of inequality shows that $m\angle 11<m\angle 6$ and $m\angle 1<m\angle 6$ .

Therefore, the angles with measures greater than $m\angle 6$ are $\angle 4,\angle 1$ , and $\angle 11$ .