Question

Question

Use the image to answer the question.

Two parallel, inclined lines labeled as m and n are separated by a distance. A diagonal line labeled as t intersects m and n at a bottom left to top right incline.

In the diagram, given m∥n , ∠8 and ∠1 are alternate exterior angles. If m∠1=9x−12 and m∠8=105° , what is the value of x?

(1 point)
Responses

52.5°
52.5°

75
75

9.7
9.7

13
13
Skip to navigation

Answer 1

Since lines \( m \) and \( n \) are parallel, the alternate exterior angles \( \angle 1 \) and \( \angle 8 \) are equal. Therefore, we can set up the equation:

\[ m\angle 1 = m\angle 8 \]

Substituting the given values:

\[ 9x - 12 = 105 \]

Next, we will solve for \( x \).

First, add 12 to both sides:

\[ 9x = 105 + 12 \] \[ 9x = 117 \]

Now, divide both sides by 9:

\[ x = \frac{117}{9} \] \[ x = 13 \]

Thus, the value of \( x \) is \( 13 \).

The correct answer is:

13