Use the image to answer the question.

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 to solve for \( x \), we need to look at the relationship between angles formed by the intersection of the slanting line with the two parallel lines.

From the given information, \( m∠5 = 112° \) and \( m∠8 = (2x + 8)° \). Angles 5 and 8 are corresponding angles formed by the slanting line and the two parallel lines, so they are equal:

\[ m∠5 = m∠8 \]

Substituting the given values, we have:

\[ 112° = (2x + 8)° \]

Now we can rearrange this equation to solve for \( x \):

1. Start with \( 112 = 2x + 8 \).
2. Subtract 8 from both sides: \[ 112 - 8 = 2x \implies 104 = 2x \]
3. Divide both sides by 2: \[ x = \frac{104}{2} = 52 \]

Thus, the equation to solve for \( x \) is:

\[ 2x + 8 = 112 \]

In the requested format, it should be written as:

\[ 2x + 8 = 112 \]

So, the final answer is:

2, 8, and 112