Question

given ( mparallel n ), find the value of ( x ).
answer attempt 1 out of 2
( x = )

Explanation:

Step1: Use the property of supplementary angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the adjacent angles \((2x + 2)^{\circ}\) and \((x + 16)^{\circ}\) are supplementary. So, \((2x+2)+(x + 16)=180\).

Step2: Simplify the equation

Combine like - terms: \(2x+x+2 + 16=180\), which gives \(3x+18 = 180\).

Step3: Solve for \(x\)

Subtract \(18\) from both sides: \(3x=180 - 18\), so \(3x=162\). Then divide both sides by \(3\): \(x=\frac{162}{3}\).

Answer:

\(x = 54\)