Question

solve for x.
x =

Explanation:

Step1: Use the property of alternate exterior angles

Since \( LM\parallel NO\), the angle \((5x - 30)^{\circ}\) and the angle adjacent to \((3x)^{\circ}\) (which is \(180 - 3x\) using the linear - pair property) are equal. So, \(5x-30=180 - 3x\).

Step2: Solve the equation for \(x\)

Add \(3x\) to both sides of the equation: \(5x+3x-30=180-3x + 3x\), which simplifies to \(8x-30 = 180\).
Add \(30\) to both sides: \(8x-30 + 30=180 + 30\), so \(8x=210\).
Divide both sides by \(8\): \(x=\frac{210}{8}=\frac{105}{4}=26.25\).

Answer:

\(26.25\)