Question

given ( l parallel m parallel n ), find the value of ( x ).
there is a diagram with three parallel lines ( l ), ( m ), ( n ) (with ( l ) top, ( m ) middle, ( n ) bottom) and a transversal intersecting them. on line ( l ), the angle with the transversal is ( (7x + 2)^circ ), and on line ( n ), the angle with the transversal is ( (6x + 7)^circ ).

Explanation:

Step1: Identify Alternate Interior Angles

Since \( l \parallel m \parallel n \), the angles \( (7x + 2)^\circ \) and \( (6x + 7)^\circ \) are alternate interior angles, so they are equal.

$$ 7x + 2 = 6x + 7 $$

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:

$$ 7x - 6x + 2 = 6x - 6x + 7 $$

$$ x + 2 = 7 $$

Subtract 2 from both sides:

$$ x + 2 - 2 = 7 - 2 $$

$$ x = 5 $$

Answer:

\( x = 5 \)