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

52.5°
52.5°

75
75

9.7
9.7

13
13
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Answer 1

Given that lines \( m \) and \( n \) are parallel and that \( \angle 8 \) and \( \angle 1 \) are alternate exterior angles, we know that these angles are equal. Therefore, we can set up the equation based on the information given:

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

Substituting the expressions for the angles, we have:

\[ 9x - 12 = 105 \]

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

\[ 9x = 105 + 12 \]

\[ 9x = 117 \]

Now, divide both sides by 9:

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

\[ x = 13 \]

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