Question

given m || n, find the value of x and y.

Explanation:

Step1: Use property of alternate - interior angles

Since \(m\parallel n\), the alternate - interior angles \((4x - 10)^{\circ}\) and \((8x-2)^{\circ}\) are supplementary. So, \((4x - 10)+(8x - 2)=180\).
\[4x-10 + 8x-2=180\]
\[12x-12 = 180\]

Step2: Solve for \(x\)

Add 12 to both sides of the equation \(12x-12 = 180\).
\[12x=180 + 12\]
\[12x=192\]
Divide both sides by 12: \(x=\frac{192}{12}=16\).

Step3: Find the value of the angle

Substitute \(x = 16\) into the expression for one of the angles. Let's use the angle \((4x - 10)^{\circ}\).
\(4x-10=4\times16-10=64 - 10=54^{\circ}\).

Step4: Use property of vertical angles

The angle \((2y)^{\circ}\) and the angle \((4x - 10)^{\circ}\) are vertical angles. Since vertical angles are equal, \(2y=4x - 10\).
Substitute \(x = 16\) into the equation \(2y=4x - 10\).
\(2y=4\times16-10\)
\(2y=54\)
Solve for \(y\): \(y = 27\).

Answer:

\(x = 16\), \(y=27\)