Question

solve for x.
x =

Explanation:

Step1: Use the property of vertical angles and linear pairs

Since \(ON\parallel PQ\), \(\angle ORL\) and \(\angle QSL\) are supplementary (consecutive interior angles). Also, \(\angle ORL=(8x + 11)^{\circ}\) and \(\angle QSL = 73^{\circ}\). The sum of consecutive - interior angles is \(180^{\circ}\).
So, \((8x + 11)+73=180\).

Step2: Simplify the equation

First, combine like terms: \(8x+84 = 180\).
Then, subtract 84 from both sides: \(8x=180 - 84\).
\(8x=96\).

Step3: Solve for \(x\)

Divide both sides by 8: \(x=\frac{96}{8}\).

Answer:

\(12\)