Question

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

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal, the sum of same - side interior angles is \(180^{\circ}\). So, \((6x + 14)+(5x+12)=180\).

Step2: Simplify the equation

Combine like terms: \(6x+5x+14 + 12=180\), which gives \(11x+26 = 180\).

Step3: Solve for \(x\)

Subtract \(26\) from both sides: \(11x=180 - 26\), so \(11x=154\). Then divide both sides by \(11\): \(x=\frac{154}{11}\).

Answer:

\(x = 14\)