Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG. The measure of angle HGF is (7y + 6)°, and the measure of angle EFG is (8y + 4)°. What is the measure of angle HGF?

Question

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

20°
28°
90°
160°

Answer 1

To find the measure of angle HGF, we can use the fact that the angles in a trapezoid add up to 360 degrees.

Given that angle EFG = (8y + 4)° and angle HGF = (7y + 6)°, we know that:

8y + 4 + 7y + 6 = 360
15y + 10 = 360
15y = 350
y = 23.33

Now, we can plug in the value of y back into the equation for angle HGF:

7(23.33) + 6 = 160.31°

Therefore, the measure of angle HGF is 160.31°.