Question

given ( l parallel m parallel n ), find the value of ( x ).

(there is a diagram showing three parallel lines ( l ), ( m ), ( n ) cut by a transversal. the angle on line ( l ) is ( (6x)^circ ), and the angle on line ( n ) is ( (7x - 20)^circ ).)

answer attempt 1 out of 2

( x = )
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Explanation:

Step1: Identify Alternate Interior Angles

Since \( l \parallel m \parallel n \), the angles \( 6x^\circ \) and \( (7x - 20)^\circ \) are alternate interior angles. Alternate interior angles are equal when lines are parallel. So, we set up the equation:
\( 6x = 7x - 20 \)

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\( 0 = x - 20 \)

Add 20 to both sides:
\( x = 20 \)

Answer:

\( x = 20 \)