Question

given m || n, find the value of x and y. (8x + 2)° m (4x + 10)° n y°

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(8x + 2=4x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(8x-4x + 2=4x-4x + 10\), which simplifies to \(4x+2 = 10\). Then subtract 2 from both sides: \(4x+2 - 2=10 - 2\), getting \(4x=8\). Divide both sides by 4: \(x=\frac{8}{4}=2\).

Step3: Find the value of \(y\)

The angle \((4x + 10)^{\circ}\) and \(y^{\circ}\) are supplementary (linear - pair of angles). Substitute \(x = 2\) into \(4x+10\), we get \(4\times2+10=18\). Since \(y+(4x + 10)=180\), then \(y=180-(4x + 10)\). Substituting \(x = 2\) gives \(y=180 - 18=162\).

Answer:

\(x = 2\), \(y=162\)