Question

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

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel n\), the angle \((7x - 1)^{\circ}\) and the angle \(111^{\circ}\) are alternate interior angles. Alternate interior angles are equal. So, \(7x-1 = 111\).

Step2: Solve the equation for \(x\)

Add \(1\) to both sides of the equation: \(7x-1 + 1=111 + 1\), which simplifies to \(7x=112\).
Divide both sides by \(7\): \(x=\frac{112}{7}\).

Answer:

\(x = 16\)