Question

Parallel lines m and n are cut by a transversal. At the intersection of line m with the transversal, the uppercase left angle is 105 degrees. At the intersection of line n with the transversal, the bottom right angle is (3 x minus 15) degrees.
What is the value of x for which m || n?

Answer 1

To determine the value of \( x \) for which lines \( m \) and \( n \) are parallel, we can use the properties of corresponding angles and transversals.

Given:
- The angle at the intersection of line \( m \) and the transversal, which is the upper left angle, measures \( 105^\circ \).
- The angle at the intersection of line \( n \) and the transversal, which is the bottom right angle, measures \( 3x - 15 \).

Since lines \( m \) and \( n \) are parallel, corresponding angles must be equal. Therefore, we can set up the equation:

\[
105^\circ = 3x - 15^\circ
\]

Now, we solve for \( x \):

1. Add \( 15 \) to both sides of the equation:

\[
105 + 15 = 3x
\]

\[
120 = 3x
\]

2. Divide both sides by \( 3 \):

\[
x = \frac{120}{3}
\]

\[
x = 40
\]

Thus, the value of \( x \) for which lines \( m \) and \( n \) are parallel is

\[
\boxed{40}.
\]