Question

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

Explanation:

Step1: Use the property of supplementary angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the consecutive - interior angles are supplementary. So \((2x + 5)+(9x+10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+9x+5 + 10=180\), which gives \(11x+15 = 180\).

Step3: Isolate the variable \(x\)

Subtract 15 from both sides: \(11x=180 - 15\), so \(11x=165\).

Step4: Solve for \(x\)

Divide both sides by 11: \(x=\frac{165}{11}\).

Answer:

\(x = 15\)