Question

Use the image to answer the question.

An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.

m∠5=112°
and m∠8=(2x+8)°
. What equation will solve for x
?

(2 points)
x°+
°=
°

Answer 1

To find the equation that will solve for \( x \), we need to identify the relationship between the angles based on their positions. Given that \( m∠5 = 112° \) and \( m∠8 = (2x + 8)° \), we can use the fact that \( ∠5 \) and \( ∠8 \) form corresponding angles with the transversal (the slanting line) intersecting the two parallel lines.

Since the lines are parallel, corresponding angles are equal. Thus, we can set up the equation:

\[
m∠5 = m∠8
\]

Substituting the values we have:

\[
112° = 2x + 8°
\]

To solve for \( x \), rearrange the equation:

\[
2x + 8 = 112
\]

Subtract 8 from both sides:

\[
2x = 112 - 8
\]

\[
2x = 104
\]

Now divide by 2:

\[
x = 52
\]

Therefore, the equation you would set up to solve for \( x \) is:

\[
112° = 2x + 8°
\]

So the finalized form of the equation is:

\[
112° = (2x + 8)°
\]

This equation can be directly used to find the value of \( x \).