Question

given m || n, find the value of x.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the angles \((8x + 9)^{\circ}\) and \(81^{\circ}\) are supplementary (linear - pair of angles formed by a transversal intersecting parallel lines).
So, \((8x + 9)+81=180\).

Step2: Simplify the equation

Combine like - terms: \(8x+(9 + 81)=180\), which gives \(8x+90 = 180\).

Step3: Solve for \(x\)

Subtract 90 from both sides: \(8x=180 - 90\), so \(8x=90\). Then divide both sides by 8: \(x=\frac{90}{8}=\frac{45}{4}=11.25\).

Answer:

\(x = 11.25\)