Question

given $m \parallel n$, find the value of $x$.
(there is a diagram showing two parallel lines m and n cut by a transversal t. on line n, the angles formed with the transversal are $(6x + 6)^circ$ and $(5x - 24)^circ$.)
answer

Explanation:

Step1: Identify Angle Relationship

Since \( m \parallel n \) and the two angles \( (6x + 6)^\circ \) and \( (5x - 24)^\circ \) are supplementary (they form a linear pair on a straight line), their sum is \( 180^\circ \). So, we set up the equation:
\( (6x + 6) + (5x - 24) = 180 \)

Step2: Simplify and Solve for \( x \)

Combine like terms:
\( 6x + 5x + 6 - 24 = 180 \)
\( 11x - 18 = 180 \)

Add 18 to both sides:
\( 11x = 180 + 18 \)
\( 11x = 198 \)

Divide both sides by 11:
\( x = \frac{198}{11} \)
\( x = 18 \)

Answer:

\( x = 18 \)