Question

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

rubric: 3pts = correct equation (equal or add to 180), 3pts correct steps to solve, 3pts = correct x value, 1pt = work

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the given angles \((7x + 9)^{\circ}\) and \((9x+5)^{\circ}\) are same - side interior angles. Same - side interior angles are supplementary, so we set up the equation \((7x + 9)+(9x + 5)=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms on the left - hand side of the equation: \(7x+9x + 9 + 5=180\), which simplifies to \(16x+14 = 180\).

Step3: Isolate the variable term

Subtract 14 from both sides of the equation: \(16x+14−14 = 180−14\), resulting in \(16x=166\).

Step4: Solve for \(x\)

Divide both sides of the equation by 16: \(x=\frac{166}{16}=\frac{83}{8}=10.375\).

Answer:

\(x = 10.375\)