Question

1. (11x - 47)° (6x - 2)° lines l and m (parallel, cut by transversal)

Explanation:

Step1: Identify the relationship

Since lines \( l \) and \( m \) are parallel, the two angles \( (11x - 47)^\circ \) and \( (6x - 2)^\circ \) are equal (corresponding angles or alternate interior angles, depending on the transversal). So we set up the equation:
\( 11x - 47 = 6x - 2 \)

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\( 11x - 6x - 47 = -2 \)
\( 5x - 47 = -2 \)

Add 47 to both sides:
\( 5x = -2 + 47 \)
\( 5x = 45 \)

Divide both sides by 5:
\( x = \frac{45}{5} \)
\( x = 9 \)

Answer:

\( x = 9 \)