Chapter 12.2, Problem 8E

1.

To determine

To find: the types of angles.

Answer to Problem 8E

The angles are corresponding angles.

Explanation of Solution

Given information :

  

The given angles in the diagram are ${32}^{\circ }$ and $8x^{\circ }$

Concept used : For a parallel line and its transversals the corresponding angles are always equal.

Explanation & Calculation:

Two angles i.e. ${32}^{\circ }$ and $8x^{\circ }$ occupy the corresponding position at intersection on the same side of the transversal.

Thus, given angles are corresponding angles.

2.

To determine

To find: an equation that relates the angle measures.

Answer to Problem 8E

  $8x^{\circ }={32}^{\circ }$

Explanation of Solution

Given information:

  

The given angles in the diagram are ${32}^{\circ }$ and $8x^{\circ }$

Calculation: Two angles i.e. ${32}^{\circ }$ and $8x^{\circ }$ occupy the corresponding position at intersection on the same side of the transversal.

Thus, given angles are corresponding angles.

So, the equation is $8x^{\circ }={32}^{\circ }$

3.

To determine

To find: The value of $x$ .

Answer to Problem 8E

  $x=4$

Explanation of Solution

Given information:

  

The given angles in the diagram are ${32}^{\circ }$ and $8x^{\circ }$

Calculation:

  $\begin{array}{l}8x^{\circ }={32}^{\circ }\\ \Rightarrow x=\frac{32}{8}\\ \Rightarrow x=4\end{array}$

Hence, the value of $x$ is $4$