Question

1. (8x - 77)° l m (3x + 38)° 7.

Explanation:

Step1: Identify the relationship

Since lines \( l \) and \( m \) are parallel, the two angles \( (8x - 77)^\circ \) and \( (3x + 38)^\circ \) are equal (alternate interior angles). So we set up the equation:
\( 8x - 77 = 3x + 38 \)

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
\( 8x - 3x - 77 = 38 \)
\( 5x - 77 = 38 \)

Add 77 to both sides:
\( 5x = 38 + 77 \)
\( 5x = 115 \)

Divide both sides by 5:
\( x = \frac{115}{5} \)
\( x = 23 \)

Answer:

\( x = 23 \)