Question

figure efgh is a trapezoid. what is the measure of angle f? \\(\bigcirc\\) \\(100^\circ\\) \\(\bigcirc\\) \\(130^\circ\\) \\(\bigcirc\\) \\(140^\circ\\) \\(\bigcirc\\) \\(150^\circ\\)

Explanation:

Step1: Recall trapezoid angle sum

In a trapezoid, the sum of interior angles is \(360^\circ\). Also, angle \(H\) is a right angle (\(90^\circ\)). So we have the equation: \(9x + 14x + 4x + 90 = 360\).

Step2: Combine like terms

Combine the \(x\) terms: \(9x + 14x + 4x = 27x\). So the equation becomes \(27x + 90 = 360\).

Step3: Solve for \(x\)

Subtract \(90\) from both sides: \(27x = 360 - 90 = 270\). Then divide by \(27\): \(x = \frac{270}{27} = 10\).

Step4: Find angle \(F\)

Angle \(F\) is \(14x^\circ\). Substitute \(x = 10\): \(14\times10 = 140^\circ\).

Answer:

\(140^\circ\) (corresponding to the option "140°")