Proofs About Angles Quick Check

Question

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Question
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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

9.7
9.7

75
75

52.5°
52.5°

13
13
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Answer 1

To determine the value of \( x \), we can use the fact that alternate exterior angles are equal when two lines are parallel. Since \( m \parallel n \), we have:

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

We know from the problem statement that:

\[ m\angle 1 = 9x - 12 \] \[ m\angle 8 = 105^\circ \]

Setting the two expressions equal to each other gives us:

\[ 9x - 12 = 105 \]

To solve for \( x \), we first add 12 to both sides:

\[ 9x = 117 \]

Next, we divide both sides by 9:

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

The value of \( x \) is \( 13 \). Therefore, the correct answer is:

13