When two <u>straight lines intersect</u>, they form two pairs of angles. The vertically opposite (non-adjacent) angles are <u>congruent</u> (equal).
From inspection of the given diagram, the <u>straight line with points C and D</u> and the <u>straight line with points F and G</u> intersect at <u>point E</u>.
Therefore, angles ∠FEC and ∠DEG are vertically opposite, and so they are equal.