Question

given $m\parallel n$, find the value of x.

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel n\), the angles \((10x + 8)^{\circ}\) and \((7x+27)^{\circ}\) are equal. So we have the equation \(10x + 8=7x + 27\).

Step2: Solve the equation for \(x\)

Subtract \(7x\) from both sides: \(10x-7x + 8=7x-7x + 27\), which simplifies to \(3x+8 = 27\).
Subtract \(8\) from both sides: \(3x+8 - 8=27 - 8\), getting \(3x=19\).
Divide both sides by \(3\): \(x=\frac{19}{1}=19\).

Answer:

\(x = 19\)