Question

given ( l parallel m parallel n ), find the value of ( x ). ((6x - 18)^circ) ((4x + 6)^circ)

Explanation:

Step1: Identify congruent angles

Since \( l \parallel m \), the given angles are alternate interior angles, so they are equal:
\( 6x - 18 = 4x + 6 \)

Step2: Isolate the variable term

Subtract \( 4x \) from both sides:
\( 6x - 4x - 18 = 6 \)
\( 2x - 18 = 6 \)

Step3: Solve for x

Add 18 to both sides, then divide by 2:
\( 2x = 6 + 18 \)
\( 2x = 24 \)
\( x = \frac{24}{2} \)

Answer:

\( x = 12 \)