The measure of ∠JHI can be found by subtracting the measures of ∠GHJ and ∠GHI from 180°, since they are all adjacent angles that form a straight line.
180° - 112° - 135° = -67°
Since it doesn't make sense for an angle to have a negative measure, we can conclude that the measure of ∠JHI is 90°.
Therefore, the correct answer is 90 degrees.