Question
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 which answer is correct and why by explaning in a 4 paragraph sentence
52.5°
52.5°
75
75
9.7
9.7
13
(1 point)
Responses which answer is correct and why by explaning in a 4 paragraph sentence
52.5°
52.5°
75
75
9.7
9.7
13
Answers
GPT-4o mini
To determine the value of \( x \) given that lines \( m \) and \( n \) are parallel and that \( \angle 8 \) and \( \angle 1 \) are alternate exterior angles, we can use the property that alternate exterior angles are equal when lines are parallel. This means that we can set the measure of angle \( 1 \) equal to the measure of angle \( 8 \).
Given that \( m \angle 1 = 9x - 12 \) and \( m \angle 8 = 105^\circ \), we can set up the equation:
\[
9x - 12 = 105
\]
To solve for \( x \), we first isolate the term with \( x \) by adding 12 to both sides of the equation:
\[
9x = 105 + 12
\]
\[
9x = 117
\]
Next, we divide both sides by 9 to find the value of \( x \):
\[
x = \frac{117}{9}
\]
\[
x = 13
\]
Thus, the solution leads us to conclude that the value of \( x \) is 13. This is supported by the property of alternate exterior angles in parallel lines, confirming that the relationships and calculations adhere to Euclidean geometry rules.
Therefore, the correct answer is **13**, as it aligns with the calculations derived from the properties of the angles formed by the parallel lines and the transversal.
Given that \( m \angle 1 = 9x - 12 \) and \( m \angle 8 = 105^\circ \), we can set up the equation:
\[
9x - 12 = 105
\]
To solve for \( x \), we first isolate the term with \( x \) by adding 12 to both sides of the equation:
\[
9x = 105 + 12
\]
\[
9x = 117
\]
Next, we divide both sides by 9 to find the value of \( x \):
\[
x = \frac{117}{9}
\]
\[
x = 13
\]
Thus, the solution leads us to conclude that the value of \( x \) is 13. This is supported by the property of alternate exterior angles in parallel lines, confirming that the relationships and calculations adhere to Euclidean geometry rules.
Therefore, the correct answer is **13**, as it aligns with the calculations derived from the properties of the angles formed by the parallel lines and the transversal.