Question

given m || n, find the value of x and y. (9x + 2)° (3x - 14)° y°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(9x + 2=3x - 14+180\) (since the non - adjacent angles formed by the intersection of a transversal with parallel lines and the linear - pair relationship).
\[9x+2=3x + 166\]

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(9x-3x+2=3x-3x + 166\), which gives \(6x+2=166\). Then subtract 2 from both sides: \(6x+2 - 2=166 - 2\), so \(6x=164\). Divide both sides by 6: \(x=\frac{164}{6}=\frac{82}{3}\).

Step3: Find \(y\)

\(y\) and \((3x - 14)\) are supplementary (linear - pair of angles). First, find the value of \(3x-14\): \(3\times\frac{82}{3}-14=82 - 14 = 68\). Since \(y+(3x - 14)=180\), then \(y=180-(3x - 14)\). Substituting \(x = \frac{82}{3}\), we get \(y = 180-68=112\).

Answer:

\(x=\frac{82}{3},y = 112\)