It is known that the line AB and CD intersect at O, OM ⊥ CD, the perpendicular point is O, OA bisects ∠ MOE, and ∠ BOD = 28 ° to find the degree of ∠ AOM ∠ COE ∠ BOE

It is known that the line AB and CD intersect at O, OM ⊥ CD, the perpendicular point is O, OA bisects ∠ MOE, and ∠ BOD = 28 ° to find the degree of ∠ AOM ∠ COE ∠ BOE

It is known that the straight line AB and CD intersect at O, OM ⊥ CD, the perpendicular point is O, OA bisects ∠ MOE, and ∠ BOD = 28 ° so ∠ AOC and ∠ BOD are diagonally opposite. It is deduced that ∠ AOC = 28 ° and OM has vertical CD, so ∠ AOC and ∠ AOM complement each other, and ∠ AOM = 62 ° because OA bisects ∠ MOE, and ∠ AOM = 62 ° it is deduced that ∠ AOE = 62

As shown in the figure, it is known that the line AB and CD intersect at the point O, OM ⊥ CD, the perpendicular foot is O, the bisector angle MOE of AB, ∠ AOC = 28 ° and the degree of ∠ AOM ∠ AOC ∠ BOE is calculated

∠AOM=90-28=62 ∠AOC=28 ∠BOE=180-62=118

As shown in the figure, the line AB and CD intersect at the point O, OE bisection ∠ BOD, of bisection ∠ Coe, ∠ AOD: ∠ BOE = 4:1, calculate the degree of ∠ EOF

Because ∠ AOD: ∠ BOE = 4:1, OE bisects ∠ BOD
So ∠ AOD: ∠ EOD = 4:1
Because ∠ AOB = 180 degree
Therefore, BOE = DOE = 30 degree
Because ∠ cod = 180 °
So ∠ COE = 180 ° - DOE = 150 °
Because of bisects Coe
So ∠ EOF = half COE = 75 degree
Bonus points

As shown in the figure, lines AB and CD intersect at point O, OE bisects ∠ BOD, of bisects ∠ Coe, ∠ AOD: ∠ BOE = 7:1, calculate the degree of ∠ AOF

∵ OE bisection ∠ BOD, ∵ DOE = ∠ BOE
∵∠AOD:∠BOE=7:1,∴∠AOD=7∠BOE.
And ∵ AOD + DOE + BOE = 180 °,
∴7∠BOE+∠BOE+∠BOE=180°,∴∠DOE=∠BOE=20°.
∴∠COE=180°-20°=160°.
∵ of bisection ∠ Coe, ∵ EOF = 1 / 2 ∠ COE = 80 °
∴∠BOF=80°-20°=60°
∴∠AOF=180°-∠BOF=120°