Question

given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify the angle relationship

Since \( m \parallel n \), the two angles \( (4x - 3)^\circ \) and \( (3x + 22)^\circ \) are alternate interior angles, so they are equal.
\[ 4x - 3 = 3x + 22 \]

Step2: Solve for \( x \)

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

Answer:

\( x = 25 \)