Question

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

Explanation:

Step1: Use the property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the consecutive - interior angles are supplementary. That is, \((4x + 15)+(9x+9)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+9x+15 + 9=180\), which gives \(13x+24 = 180\).

Step3: Solve for \(x\)

Subtract 24 from both sides of the equation: \(13x=180 - 24\), so \(13x=156\).
Divide both sides by 13: \(x=\frac{156}{13}\).

Answer:

\(x = 12\)