Yes, they are congruent.
Work Step by Step
We know that the angles form a linear pair, so they are supplementary. In other words, they will add up to 180 degrees. Given that the angles fall in the range of 0 to 180 degrees, the angles will be congruent if and only if both of the angles are equal to 90 degrees. It is given that one of the angles is 90 degrees, which means the other angle is 180-90 = 90 degrees as well. Thus, they are congruent.