Question

what is the value of x? 25 (there is a diagram with two parallel lines m and n cut by a transversal l. the angle between l and m is 45 degrees, and the angle between l and n is (2x - 5) degrees)

Explanation:

Step1: Identify the angle relationship

Since lines \( m \) and \( n \) are parallel, and the transversal \( l \) cuts them, the given angles \( 45^\circ \) and \( (2x - 5)^\circ \) are equal (corresponding angles or alternate interior angles, depending on the position, but here they are equal as the lines are parallel). So we set up the equation: \( 2x - 5 = 45 \)

Step2: Solve for \( x \)

Add 5 to both sides of the equation: \( 2x = 45 + 5 \)
\( 2x = 50 \)
Divide both sides by 2: \( x = \frac{50}{2} \)
\( x = 25 \)

Answer:

\( x = 25 \)