Question

solve for x.

x =

Explanation:

Step1: Use the property of corresponding angles

Since \(NO\parallel PQ\), \(\angle LRN\) and \(\angle LSP\) are corresponding angles. And \(\angle LRN=(134 - 2x)^{\circ}\), \(\angle LSP=(140 - 5x)^{\circ}\). Also, \(\angle LRN\) and \((140 - 5x)^{\circ}\) are vertical - angle - related. According to the property of parallel lines (corresponding angles are equal), we have \(134-2x = 140 - 5x\).

Step2: Solve the equation for \(x\)

Add \(5x\) to both sides of the equation \(134-2x = 140 - 5x\):
\(134-2x + 5x=140-5x + 5x\), which simplifies to \(134 + 3x=140\).
Subtract \(134\) from both sides: \(3x=140 - 134\), so \(3x = 6\).
Divide both sides by \(3\): \(x=\frac{6}{3}=2\).

Answer:

\(2\)