Question

given ( l parallel m parallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of parallel lines

When \(l\parallel m\parallel n\), the sum of the angle \((8x + 17)^{\circ}\) and \((5x-6)^{\circ}\) is \(180^{\circ}\) (consecutive interior angles). So, we get the equation \(8x+17 + 5x-6=180\).

Step2: Simplify the equation

Combine like - terms: \((8x + 5x)+(17 - 6)=180\), which simplifies to \(13x+11 = 180\).

Step3: Solve for \(x\)

Subtract \(11\) from both sides: \(13x=180 - 11\), so \(13x=169\). Then divide both sides by \(13\): \(x=\frac{169}{13}\).

Answer:

\(x = 13\)