figure efgh is a trapezoid. what is the measure of angle f? (9x)° (14x)° (4x)° 100° 130° 140° 150°

Explanation:

Step1: Recall angle - sum property of trapezoid

The sum of the interior angles of a quadrilateral is $360^{\circ}$. In trapezoid EFGH, $\angle E=(9x)^{\circ}$, $\angle F=(14x)^{\circ}$, $\angle G=(4x)^{\circ}$, and $\angle H = 90^{\circ}$. So, $9x+14x + 4x+90=360$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $(9 + 14+4)x+90=360$, which simplifies to $27x+90 = 360$.

Step3: Solve for $x$

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

Step4: Find the measure of $\angle F$

Since $\angle F=(14x)^{\circ}$ and $x = 10$, then $\angle F=14\times10=140^{\circ}$.

Answer:

$140^{\circ}$