Question

1. for what value of x is line m parallel to line n? enter your answer in the box. x =

Explanation:

Step1: Identify the relationship

For lines \( m \) and \( n \) to be parallel, the corresponding angles (or supplementary angles in this case) should be equal. The angle \( 105^\circ \) and \( (10x + 15)^\circ \) are equal (corresponding angles or alternate interior angles, depending on the transversal). So we set up the equation:
\( 10x + 15 = 105 \)

Step2: Solve for \( x \)

Subtract 15 from both sides:
\( 10x = 105 - 15 \)
\( 10x = 90 \)

Divide both sides by 10:
\( x = \frac{90}{10} \)
\( x = 9 \)

Answer:

\( x = 9 \)