Question

given (mparallel n), find the value of (x).

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((6x + 6)^{\circ}\) and \((5x-24)^{\circ}\) are supplementary (linear - pair of angles), so their sum is \(180^{\circ}\). We set up the equation \(6x + 6+5x-24=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((6x + 5x)+(6 - 24)=180\), which simplifies to \(11x-18 = 180\).

Step3: Isolate the variable term

Add 18 to both sides of the equation: \(11x-18 + 18=180 + 18\), resulting in \(11x=198\).

Step4: Solve for \(x\)

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

Answer:

\(18\)