In the figure, p || q and r is the transversal. If OA and OB are bisectors of the interior angles, which of these describes angle AOB?

To determine the relationship between angle AOB and the given conditions, we need to apply the properties of parallel lines and transversals.

1. When a transversal intersects two parallel lines, corresponding angles are congruent. This means that if p || q and r is the transversal, then angle AOB and angle AOC are congruent.
2. With OA and OB being bisectors of the interior angles, we know that angle OAC is congruent to angle OCA, and angle OBC is congruent to angle OCB.

Combining these properties, we can conclude that angle AOB is the sum of angle AOC and angle BOC. Since angles OAC and OBC are congruent to angles OCA and OCB, respectively, we can simplify the sum:

angle AOB = angle AOC + angle BOC
= (angle OAC + angle OCA) + (angle OBC + angle OCB)
= (angle OAC + angle OCA) + (angle OAC + angle OCB)
= 2 * angle OAC + angle OCB

Therefore, the description that describes angle AOB is that it is equal to twice the measure of angle OAC plus the measure of angle OCB.