Question
Proofs About Angles Quick Check
2 of 52 of 5 Items
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
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Answers
GPT-4o mini
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**.
\[
m\angle 1 = m\angle 8
\]
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**.