Question

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

Explanation:

Step1: Use the property of corresponding angles

Since \(m\parallel n\), the angle \(120^{\circ}\) and \((5x + 20)^{\circ}\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So, \(5x+20 = 120\).

Step2: Solve the equation for \(x\)

Subtract \(20\) from both sides of the equation: \(5x+20-20=120 - 20\), which simplifies to \(5x=100\).
Then divide both sides by \(5\): \(x=\frac{100}{5}\).

Answer:

\(x = 20\)