Question

given m∥n, find the value of x.

Explanation:

Step1: Identify alternate interior angles

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (4x - 3)^\circ \) and \( (3x + 22)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel.
So, we set up the equation: \( 4x - 3 = 3x + 22 \)

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 4x - 3x - 3 = 3x - 3x + 22 \)
Simplify: \( x - 3 = 22 \)
Add 3 to both sides: \( x - 3 + 3 = 22 + 3 \)
Simplify: \( x = 25 \)

Answer:

\( x = 25 \)