Question

if $overline{fg}$ is not parallel to $overline{de}$, what is $mangle f?
e
40^{circ}
d
g
mangle f=square^{circ}$

Explanation:

Step1: Recall angle - sum property of a trapezoid

The sum of the interior angles of a quadrilateral is 360°. In trapezoid DEGF, we know one angle ∠E = 40°. Since DE∥FG (the arrow - heads on the lines indicate parallelism), ∠E and ∠D are supplementary (same - side interior angles between parallel lines), so ∠D=180 - 40=140°. Also, ∠G and ∠D are supplementary, so ∠G = 40°.

Step2: Calculate ∠F

Let ∠F=x. Using the angle - sum property of a quadrilateral ∠E+∠D+∠G+∠F = 360°. Substitute ∠E = 40°, ∠D = 140°, and ∠G = 40° into the equation: 40+140 + 40+x=360. Simplify the left - hand side: 220+x=360. Solve for x: x=360 - 220=140.

Answer:

140