Question

Use the diagram. For lines $m$and $n$to be parallel, what must the value of $x$be?

1. Tell whether the labelled angles are corresponding, alternate interior, or alternate exterior angles.
2. Write an equation that relates the angles measures.
3. Solve the equation for $x$.

Short answer

1. The angles $32°$and $8x°$ arecorresponding angles.
2. The required equation is $8x{}^{\circ }=32°$.
3. The value of $x$ is $x=4$.

Step-by-step solution

1.Step 1. Given Information.

The provided diagram is,

Step 2. Definition of corresponding angles.

When two lines are crossed by another line, it is known as transversal.Corresponding angles are angles that are at the same relative position at each intersection.

Step 3. Explanation.

In the given figure, two parallel lines are intersected by a transversal. Since the angles $32°$ and $8x°$ occupy the corresponding position at intersection on the same side of the transversal.

Step 4. Conclusion.

The angles $32°$and $8x°$ arecorresponding angles.

2.Step 1. Given Information.

The provided diagram is,

Step 2. Concepts used.

When two lines are crossed by another line, it is known as transversal.Corresponding angles are angles that are at the same relative position at each intersection. The measure of two corresponding angles is equal.

Step 3. Explanation.

Two angles $32°$and $8x°$occupy the corresponding position at intersection on the same side of the transversal.

Thus, given angles are corresponding angles. So, the measures must be equal, that is, $8x{}^{\circ }=32°$.

Step 4. Conclusion.

The required equation is $8x{}^{\circ }=32°$.

3.Step 1. Given Information.

The provided diagram is,

Step 2. Calculation.

The value of $x$ is,

$\begin{array}{c}8x°=32°\\ \frac{8x}{8}=\frac{32}{8}\\ x=4\end{array}$

Step 3. Conclusion.

The value of$x$ is $x=4$.