Question

line ( n ) intersects lines ( l ) and ( m ), forming the angles shown in the diagram below. which value of ( x ) would prove ( l parallel m )? 1) ( 2.5 ) 2) ( 4.5 ) 3) ( 6.25 ) 4) ( 8.75 )

Explanation:

Step1: Use the property of parallel lines

When \( l\parallel m \), the corresponding angles are equal. So, \( 6x + 42=18x-12 \).

Step2: Solve the equation for \( x \)

Subtract \( 6x \) from both sides: \( 42 = 12x-12 \).
Add \( 12 \) to both sides: \( 42 + 12=12x \), i.e., \( 54 = 12x \).
Divide both sides by \( 12 \): \( x=\frac{54}{12}=4.5 \).

Answer:

1. \( 4.5 \)