Question

given ( mparallel 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 \(t\), the sum of same - side interior angles is \(180^{\circ}\). So, \((9x - 9)+(x - 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(9x-9+x - 1=(9x+x)+(-9 - 1)=10x-10\). The equation becomes \(10x-10 = 180\).

Step3: Solve for \(x\)

Add \(10\) to both sides of the equation: \(10x-10 + 10=180 + 10\), which gives \(10x=190\). Then divide both sides by \(10\): \(x=\frac{190}{10}=19\).

Answer:

\(x = 19\)