Final answer:
Angle OAB in a rectangle with diagonals intersecting at O is equal to 102 degrees, as it is congruent to the alternate interior angle, assuming both diagonals intersect at point O.
Step-by-step explanation:
To find the measure of angle OAB in rectangle ABCD with diagonals intersecting at O, we utilize the fact that the diagonals of a rectangle are congruent and bisect each other.
Given that angle COD equals 78 degrees, we know that angle COA is also 78 degrees because diagonals of a rectangle create congruent adjacent angles at the point of intersection.
Since angle COA and angle AOB form a straight line, they must sum up to 180 degrees. Hence, the measure of angle AOB is 180 - 78, which equals 102 degrees.
However, since angle OAB is the alternate interior angle to angle AOB (as sides AB and CD are parallel), angle OAB is also equal to 102 degrees, assuming the question meant the diagonal of the rectangle ABCD intersects at O. Thus, the measure of angle OAB is 102 degrees.