Question

complete the steps to find the value of x.
9
65 + \square = 180
11x + \square = 180
11x = \square
x = \square

Explanation:

Step1: Use the property of same - side interior angles

Since the two lines are parallel, the sum of \(65^{\circ}\) and \(\angle5\) is \(180^{\circ}\). Also, \(\angle5=(11x - 17)^{\circ}\). So \(65+(11x - 17)=180\).

Step2: Simplify the equation

Expand the left - hand side: \(65 + 11x-17=180\), which simplifies to \(11x+48 = 180\).

Step3: Solve for \(11x\)

Subtract \(48\) from both sides of the equation \(11x+48 = 180\). We get \(11x=180 - 48\), so \(11x = 132\).

Step4: Solve for \(x\)

Divide both sides of the equation \(11x = 132\) by \(11\). Then \(x=\frac{132}{11}=12\).

Answer:

\(65+(11x - 17)=180\); \(11x + 48=180\); \(11x=132\); \(x = 12\)