Question

given m || n, find the value of x and y. (8x + 2)° (4x + 10)° 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 vertical - angles. Vertical angles are equal. Substitute \(x = 2\) into \(4x+10\): \(4\times2+10=8 + 10=18\). So \(y = 18\).

Answer:

\(x = 2,y = 18\)