Question

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

Explanation:

Step1: Use the property of supplementary angles

Since \(m\parallel n\), the sum of \((4x - 17)^{\circ}\) and \(65^{\circ}\) is \(180^{\circ}\). So, \(4x-17 + 65=180\).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \(4x+(65 - 17)=180\), which gives \(4x + 48=180\).

Step3: Solve for \(x\)

Subtract \(48\) from both sides: \(4x=180 - 48\), so \(4x=132\). Then divide both sides by \(4\): \(x=\frac{132}{4}\).

Answer:

\(x = 33\)