Question

directions: if l || m, solve for x.

1. (9x + 2)°, 119° (diagram: parallel lines l, m with transversal; handwritten: 9x+2 = 119, 9x = 117, x=13)
2. (12x - 8)°, 104° (diagram: parallel lines l, m with transversal)

Explanation:

Problem 5:

Step1: Identify angle relationship

Since \( l \parallel m \), the angle \( (9x + 2)^\circ \) and \( 119^\circ \) are equal (corresponding angles or alternate interior angles, depending on the diagram). So we set up the equation:
\( 9x + 2 = 119 \)

Step2: Solve for \( x \)

Subtract 2 from both sides:
\( 9x = 119 - 2 \)
\( 9x = 117 \)

Divide both sides by 9:
\( x = \frac{117}{9} \)
\( x = 13 \)

Step1: Identify angle relationship

Since \( l \parallel m \), the angle \( (12x - 8)^\circ \) and \( 104^\circ \) are equal (corresponding angles or alternate interior angles, depending on the diagram). So we set up the equation:
\( 12x - 8 = 104 \)

Step2: Solve for \( x \)

Add 8 to both sides:
\( 12x = 104 + 8 \)
\( 12x = 112 \)

Divide both sides by 12:
\( x = \frac{112}{12} \)
Simplify the fraction:
\( x = \frac{28}{3} \approx 9.33 \) (or keep as a fraction)

Answer:

\( x = 13 \)

Problem 6: