Question

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

Explanation:

Step1: Recall sum of angles in trapezoid

The sum of the interior angles of a quadrilateral is $360^{\circ}$. In trapezoid EFGH, we have angles $(9x)^{\circ}$, $(14x)^{\circ}$, $(4x)^{\circ}$ and a right - angle which is $90^{\circ}$. 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 measure of angle F

Angle F is $(14x)^{\circ}$. Substitute $x = 10$ into the expression for angle F. So, the measure of angle F is $14\times10=140^{\circ}$.

Answer:

$140^{\circ}$