#### Answer

$\angle$GOH = 63$^{\circ}$
$\angle$AOC = 80$^{\circ}$
$\angle$GOF = 80$^{\circ}$
$\angle$EOF = 37$^{\circ}$

#### Work Step by Step

$\angle$COE and $\angle$GOH are vertical angles. This means that they are equal.
Therefore $\angle$GOH = 63$^{\circ}$
$\angle$AOH and $\angle$EOF are vertical angles. This means that they are equal.
Therefore $\angle$EOF = 37$^{\circ}$
The sum of $\angle$COE, $\angle$AOC, and $\angle$AOH eqeals 180$^{\circ}$. This is due to $\angle$EOH being a Straight Angle.
$\angle$AOC = 180$^{\circ}$ - (63$^{\circ}$ + 37$^{\circ}$)
$\angle$AOC = 180$^{\circ}$ - 100$^{\circ}$
$\angle$AOC = $^{\circ}$80
$\angle$AOC and $\angle$GOF are vertical angles. This means that they are equal.
Therefore $\angle$GOF = 80$^{\circ}$