Question

multiple choice 1 point
lines j and k are parallel in the figure shown. if f = 9b, what is the value of 2d?
324
162
18
36

Explanation:

Step1: Use the property of supplementary angles

Since \(b + f=180^{\circ}\) (supplementary angles) and \(f = 9b\), substitute \(f\) into the equation:
\(b+9b=180^{\circ}\)
\(10b = 180^{\circ}\)
\(b = 18^{\circ}\)

Step2: Use the property of alternate - interior angles

Since lines \(j\) and \(k\) are parallel, \(d\) and \(b\) are related by the property of consecutive - interior angles. In fact, \(d=180 - b\) (because \(b\) and \(d\) are consecutive - interior angles for parallel lines \(j\) and \(k\) cut by transversal \(l\)).
Since \(b = 18^{\circ}\), then \(d=180 - 18=162^{\circ}\)

Step3: Calculate \(2d\)

\(2d=2\times162 = 324^{\circ}\)

Answer:

324