Question

given ( l parallel m parallel n ), find the value of ( x ).
there is a diagram with three parallel lines ( l ), ( m ), ( n ) ( ( l ) is the top one, ( m ) is the middle one, ( n ) is the bottom one) and a transversal intersecting them. the angle formed by the transversal and line ( l ) is ( (9x - 19)^circ ), and the angle formed by the transversal and line ( n ) is ( 35^circ ).

Explanation:

Step1: Identify Alternate Interior Angles

Since \( l \parallel m \parallel n \), the angle \( (9x - 19)^\circ \) and \( 35^\circ \) are alternate interior angles, so they are equal.

$$ 9x - 19 = 35 $$

Step2: Solve for \( x \)

Add 19 to both sides:

$$ 9x = 35 + 19 $$

$$ 9x = 54 $$

Divide both sides by 9:

$$ x = \frac{54}{9} $$

$$ x = 6 $$

Answer:

\( x = 6 \)