Question

question given ( m parallel n ), find the value of ( x ) and ( y ).

Explanation:

Step1: Use the property of parallel lines

Since \(m\parallel n\), the angles \((8x + 10)^{\circ}\) and \((3x+5)^{\circ}\) are supplementary. So, \((8x + 10)+(3x + 5)=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(8x+3x+10 + 5=180\), which simplifies to \(11x+15 = 180\).
Subtract 15 from both sides: \(11x=180 - 15=165\).
Divide both sides by 11: \(x=\frac{165}{11}=15\).

Step3: Find the value of \(y\)

\(y\) and \((3x + 5)\) are alternate - interior angles. Since \(x = 15\), then \(3x+5=3\times15+5=45 + 5=50\). So \(y = 50\).

Answer:

\(x = 15\) and \(y=50\)