Chapter 3, Problem 12CT

To determine

To show: that $\overline{EB}\text{and }\overline{DF}$ must be parallel to each other with the help of given figure.

Answer to Problem 12CT

  $\overline{EB}\text{and }\overline{DF}$ is parallel to each other due to:

  $\angle CBE=\angle 2={72}^{\circ }$ because they are alternate interior angles,

  $\angle 1=\angle 2={72}^{\circ }$ because they are same-side interior angles,

  $\angle 3=\angle 5={36}^{\circ }$ because they are two angles in corresponding position relative to the two lines $EB\parallel DF$

Explanation of Solution

Given information:

The system of equation:

Calculation:

Considering the following figure:

In above figure line segment $ABCDE$ is a regular polygon.

The measure of $\angle CBE={72}^{\circ }$

Line segment $EB\parallel DF$ must be parallel because of the following reasons

  $\angle CBE=\angle 2={72}^{\circ }$ because they are alternate interior angles,

  $\angle 1=\angle 2={72}^{\circ }$ because they are same-side interior angles,

  $\angle 3=\angle 5={36}^{\circ }$ because they are two angles in corresponding position relative to the two lines $EB\parallel DF$

Therefore, $EB\parallel DF$ must be parallel.