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 \(b\) and \(f\) are supplementary angles (because \(j\parallel k\) and \(l\) is a transversal), we have \(b + f=180^{\circ}\). Given \(f = 9b\), substitute \(f\) into the equation: \(b+9b=180^{\circ}\).

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Step2: Use the property of alternate - interior angles

Since \(j\parallel k\) and \(l\) is a transversal, \(b\) and \(d\) are alternate - interior angles. So \(b=d\) (alternate - interior angles are equal). Since \(b = 18^{\circ}\), then \(d=18^{\circ}\).

Step3: Calculate \(2d\)

Multiply \(d\) by \(2\): \(2d=2\times18^{\circ}=36^{\circ}\)

Answer:

36