Question

Parallel lines m and n are cut by transversal l. On line m where it intersects with line l, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: blank, blank, 45 degrees, blank. On line n where it intersects with line l, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are blank, (2 x minus 5) degrees, blank, blank.
What is the value of x?

Answer 1

To solve for \( x \), we need to understand the relationships between the angles formed when parallel lines are cut by a transversal.

According to the problem, we have:

- On line \( m \) there are angles labeled clockwise:
1. Angle 1: blank
2. Angle 2: blank
3. Angle 3: 45 degrees
4. Angle 4: blank

- On line \( n \) there are angles labeled clockwise:
1. Angle 1: blank
2. Angle 2: \( (2x - 5) \) degrees
3. Angle 3: blank
4. Angle 4: blank

Since lines \( m \) and \( n \) are parallel, we can use the properties of corresponding angles and alternate interior angles.

1. The angle corresponding to the 45 degrees angle on line \( m \) would be the angle at line \( n \) that matches its position. From the layout:
- Angle 3 on line \( m \) is 45 degrees, so the corresponding angle on line \( n\) (which is the angle directly across the transversal from angle 3) will also be 45 degrees.

2. Therefore, we can equate the corresponding angle from line \( n \):
\[
2x - 5 = 45
\]

3. Now, solve for \( x \):
\[
2x - 5 + 5 = 45 + 5
\]
\[
2x = 50
\]
\[
x = \frac{50}{2} = 25
\]

Thus, the value of \( x \) is \( \boxed{25} \).