Chapter 7.1, Problem 60SPR

To determine

To list: The angles that satisfy the given condition.

Answer to Problem 60SPR

The angles with measures less than $m\angle 5$ are $\angle 2,\angle 10,\angle 7$ , and $\angle 8$ .

Explanation of Solution

Given:

The given condition is “measure less than $m\angle 5$ .”

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 $\Delta CBD$ , corresponding remote interior angles of $\angle 5$ are $\angle 2$ and $\angle 10$ .

Thus, exterior angle inequality shows that $m\angle 2<m\angle 5$ and $m\angle 10<m\angle 5$ .

In $\Delta ABD$ , corresponding remote interior angle of $\angle 10$ are $\angle 8$ and $\angle 7$ .

Transitive property of inequality shows that $m\angle 7<m\angle 5$ and $m\angle 8<m\angle 5$ .

Therefore, the angles with measures less than $m\angle 5$ are $\angle 2,\angle 10,\angle 7$ , and $\angle 8$ .