Question

Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (5y − 2)°, and the measure of angle EFG is (4y + 4)°. What is the measure of angle HGF?

Trapezoid E F G H is drawn with parallel bases E H and F G.

20°
28°
78°
90°

Answer 1

To find the measure of angle HGF, we need to set up an equation based on the fact that angles in a trapezoid add up to 360 degrees.

Since EFGH is an isosceles trapezoid, we know that the base angles (angle EFG and angle HGF) are congruent. Therefore, we can set up the following equation:

(5y - 2) + (4y + 4) + (5y - 2) + (4y + 4) = 360
18y + 4 = 360
18y = 356
y = 19.78

Now, we can plug this value of y back into the measure of angle HGF:

(5 * 19.78 - 2) = 97.9 degrees

Therefore, the measure of angle HGF is 97.9 degrees. Which is closest to 98°.