Question

given ( l parallel m parallel n ), find the value of ( x ).
diagram: three parallel lines ( l ) (top), ( m ) (middle), ( n ) (bottom) cut by a transversal. angle between ( l ) and ( m ): ( (9x - 19)^circ ); angle between ( m ) and ( n ): ( 35^circ ). below: \answer attempt 1 out of 2\ and ( x = ) input box with \submit answer\ button.

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:

\( x = 6 \)