Question

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

Explanation:

Step1: Use the property of same - side interior angles

When \(m\parallel n\), the sum of same - side interior angles is \(180^{\circ}\). 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 \(9\): \(x=\frac{207}{9}=21\).

Answer:

\(x = 21\)