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

The sum of the measures of ∠GHJ and ∠JHI is the measure of the obtuse angle ∠GHI. If ∠GHI has a measure of 135° and ∠GHJ has a measure of 112°, then ∠GHI - ∠GHJ = ∠JHI.

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