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.

Question

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

Answer 1

To solve for \( x \), we can utilize the relationships between the angles formed by a transversal (the slanting line) intersecting two parallel lines.

Given:

• \( m∠5 = 112^\circ \)
• \( m∠8 = (2x + 8)^\circ \)

Since angle \( 5 \) and angle \( 8 \) are corresponding angles formed by the transversal and the two parallel lines, they are equal. Therefore, we can set up the following equation:

\[ m∠5 = m∠8 \]

Substituting the given values:

\[ 112^\circ = 2x + 8^\circ \]

Now, we can solve for \( x \). First, subtract \( 8 \) from both sides:

\[ 112 - 8 = 2x \]

This simplifies to:

\[ 104 = 2x \]

Next, divide both sides by \( 2 \):

\[ x = \frac{104}{2} = 52 \]

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

\[ 112 = 2x + 8 \]