In the figure, AOC and BOE are straight lines. $\angle AOB = 285^\circ$. Find $\angle EOD$.

1. Find the interior angle AOB

Angles at a point sum to $360^\circ$.
Interior $\angle AOB = 360^\circ - 285^\circ = 75^\circ$

2. Find angle BOC

AOC is a straight line, so angles on a straight line sum to $180^\circ$.
$\angle BOC = 180^\circ - \angle AOB = 180^\circ - 75^\circ = 105^\circ$

3. Find angle EOD

BOE is a straight line, so angles on a straight line sum to $180^\circ$.
$\angle EOD + \angle COD + \angle BOC = 180^\circ$
$\angle EOD + 44^\circ + 105^\circ = 180^\circ$
$\angle EOD = 180^\circ - 149^\circ = 31^\circ$