Question

directions: if ( l parallel m ), solve for ( x ).

1. diagram: two parallel lines ( l ) (top) and ( m ) (bottom), cut by a transversal. on line ( l ), an angle ( (9x + 2)^circ ) (left, alternate to the angle on line ( m ) which is ( 119^circ ))

Explanation:

Step1: Identify angle relationship

Since \( l \parallel m \), the angle \( (9x + 2)^\circ \) and \( 119^\circ \) are corresponding angles (or alternate exterior angles, depending on the diagram), so they are equal. Thus, \( 9x + 2 = 119 \).

Step2: Solve for \( x \)

Subtract 2 from both sides: \( 9x = 119 - 2 = 117 \).
Divide both sides by 9: \( x = \frac{117}{9} = 13 \).

Answer:

\( x = 13 \)