Answer
$\angle FOA$ and $\angle BOC$ are supplementary.
Work Step by Step
Using the result from Exercise 42, we can state the following:
$\triangle AOF \cong \triangle AOE$
By a similar argument:
$\triangle BOF \cong \triangle BOD$
$\triangle DOC \cong \triangle EOC$
Therefore:
$\angle FOA \cong \angle EOA$
$\angle BOF \cong \angle BOD$
$\angle DOC \cong \angle EOC$
Then:
$\angle FOA + \angle EOA +\angle BOF + \angle BOD + \angle DOC + \angle EOC = 360^{\circ}$
$\angle FOA + \angle FOA +\angle BOD + \angle BOD + \angle DOC + \angle DOC = 360^{\circ}$
$2\angle FOA +2\angle BOD + 2\angle DOC = 360^{\circ}$
$\angle FOA +\angle BOD + \angle DOC = 180^{\circ}$
$\angle FOA +\angle BOC = 180^{\circ}$
Therefore, $\angle FOA$ and $\angle BOC$ are supplementary.
