Question

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

Explanation:

Step1: Identify Alternate Interior Angles

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (3x + 7)^\circ \) and \( (x + 19)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So, we set up the equation:
\( 3x + 7 = x + 19 \)

Step2: Solve for \( x \)

Subtract \( x \) from both sides:
\( 3x - x + 7 = 19 \)
\( 2x + 7 = 19 \)

Subtract 7 from both sides:
\( 2x = 19 - 7 \)
\( 2x = 12 \)

Divide both sides by 2:
\( x = \frac{12}{2} \)
\( x = 6 \)

Answer:

\( x = 6 \)