Question

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

Explanation:

Step1: Use the property of supplementary angles

Since \(m\parallel n\), the two angles \((2x - 29)^{\circ}\) and \((7x + 2)^{\circ}\) are supplementary. So, \((2x-29)+(7x + 2)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+7x-29 + 2=180\), which simplifies to \(9x-27 = 180\).

Step3: Solve for \(x\)

Add \(27\) to both sides: \(9x=180 + 27=207\). Then divide both sides by \(9\): \(x=\frac{207}{9}=17\).

Answer:

\(x = 17\)