Basic College Mathematics (9th Edition)

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