Chapter 5, Problem 19MCQ

To determine

To Find: The list of the angle that satisfy the given condition.

Answer to Problem 19MCQ

The angle that are less than $\angle 10$ are $\angle 6$ and $\angle 2$ .

Explanation of Solution

Given:

The given condition is that angle measures less than $m\angle 10$ .

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

By the exterior angle inequality theorem the exterior angle $m\angle 10$ is more than the remote interior angle $\angle 6,\angle 2$ .

Also,

  $\begin{array}{l}m\angle 10+m\angle 1=180°\\ m\angle 6+m\angle 2+m\angle 1=180°\end{array}$

Therefore, $\angle 10$ is less than the each of the individual angle in the exterior angle $m\angle 10>m\angle 6,m\angle 10>m\angle 2$ .

Thus, the angle that are less than $\angle 10$ are $\angle 6$ and $\angle 2$ .