An obtuse angle GHI has a measure of 135°. It contains adjacent angles GHJ and JHI. Angle GHJ has a measure of 112°. What is the measure of angle JHI?

The sum of angle GHJ and angle JHI is equal to the measure of angle GHI.

Therefore, the measure of angle JHI is 135° - 112° = <<135-112=23>>23°. Answer: \boxed{23}.