Question

practice with lines cut by a transversal.
what is the value of x?
(there is a diagram with lines l, m, n where line l is a transversal, intersecting line m and line n. at the intersection with line m, there is a 45° angle, and at the intersection with line n, there is a (2x - 5)° angle.)

Explanation:

Step1: Identify angle relationship

Lines \( m \) and \( n \) are parallel, cut by transversal \( l \). The \( 45^\circ \) angle and \( (2x - 5)^\circ \) angle are alternate interior angles, so they are equal.
Thus, \( 2x - 5 = 45 \).

Step2: Solve for \( x \)

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

Answer:

\( 25 \)