Chapter 12, Problem 9MCQ

To determine

To find: The angles in the diagram corresponding, alternate interior,or alternate exterior angles.

Answer to Problem 9MCQ

  $\angle 2\text{ and }\angle 7$ is an alternate interior angle.

Explanation of Solution

Given information: Following the Diagram $\angle 2\text{ and }\angle \text{7}$

Calculation:

According to the diagram corresponding angles are,

  $\begin{array}{l}\angle 1,\angle 5\\ \angle 2,\angle 6\\ \angle 3,\angle 7\\ \angle 4,\angle 8\end{array}$

And the vertically opposite angles are

  $\begin{array}{l}\angle 1,\angle 4\\ \angle 2,\angle 3\\ \angle 5,\angle 8\\ \angle 7,\angle 6\end{array}$

So the angles are,

  $\begin{array}{l}\angle 1=\angle 4=\angle 5=\angle 8\\ \text{and}\\ \angle 3=\angle 2=\angle 6=\angle 7\end{array}$ (using the corresponding and vertically opposite angles)

So, $\angle 2\text{ and }\angle \text{7 }$ are equal and $\angle 2\text{ and }\angle \text{7}$ is an interior angles