Math -geometry~hexagon diagonals

Question

Given regular hexagon BCDEFG with diagonal EG-

find m<FEG

Answer 1

draw a diagram

the number of degrees in any polynomial is found by using the formula (n-2)(180) where n is the number of sides of the polynomial

(n-2)(180)=(6-2)(180)=4*180=720°

720/6=120° in each of the six angles

draw diagonal EG

angle F contains 120°

FG is congruent to FE (regular hexagon)

triangle FGE is isosceles

angle EGF and angle GEF are congruent because the base angles of an isosceles triangle are congruent

180-120=60° left for angles EGF and GEF

60/2=30° for both angle EGF and angle GEF (FEG)

Answer 2

Draw and label a diagram!

m∠EFG = 150º

m∠GEF + m∠EGF = 30º