Question

In the diagram, given m || n, 28 and 21 are alternate exterior angles. If m/1 = 9x - 12 and m/8 = 105°, what is the value of x?

75
9.7
13
52.5°

Answer 1

Since lines \( m \) and \( n \) are parallel and \( 28^\circ \) and \( 21^\circ \) are alternate exterior angles, we can set up the equation:

\[
28^\circ = 21^\circ
\]

However, the question gives us expressions for angles in terms of \( x \):

1. \( m/1 = 9x - 12 \)
2. \( m/8 = 105^\circ \)

We first need to understand which specific angles \( m/1 \) and \( m/8 \) refer to based on the context of the problem. Assuming \( m/8 \) (which is given as \( 105^\circ \)) refers to an angle that is equated with the previously defined angles, since alternate exterior angles should equal each other (as mentioned but followed by the context misunderstanding).

Thus, based on the information given:

1. Setting \( m/1 = 9x - 12 \) equal to \( 105^\circ \):

\[
9x - 12 = 105
\]

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

\[
9x = 105 + 12
\]
\[
9x = 117
\]
\[
x = \frac{117}{9}
\]
\[
x = 13
\]

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

Thus, the answer is:

\[
\boxed{13}
\]