Question

solve for x. x =

Explanation:

Step1: Use the property of alternate interior angles

Since \( LM\parallel NO\), the angles \((5x - 30)^{\circ}\) and \((3x)^{\circ}\) are alternate interior angles. Alternate interior angles are equal. So, \(5x-30 = 3x\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides of the equation: \(5x-3x - 30=3x - 3x\), which simplifies to \(2x-30 = 0\).
Add \(30\) to both sides: \(2x-30 + 30=0 + 30\), getting \(2x=30\).
Divide both sides by \(2\): \(x=\frac{30}{2}\).

Answer:

\(15\)