Question

given ( m parallel n ), find the value of ( x ).
diagram: two parallel lines ( m ) (top) and ( n ) (bottom), cut by a transversal. angle on line ( m ): ( (4x + 7)^circ ); angle on line ( n ): ( (5x - 19)^circ ).
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify the angle relationship

Since \( m \parallel n \), the two angles \( (4x + 7)^\circ \) and \( (5x - 19)^\circ \) are alternate interior angles, so they are equal.
\[ 4x + 7 = 5x - 19 \]

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:
\[ 7 = x - 19 \]
Add 19 to both sides:
\[ x = 7 + 19 \]
\[ x = 26 \]

Answer:

\( 26 \)