To find the measure of ∠JHI, we can use the fact that the sum of the measures of adjacent angles around point H must equal the measure of the obtuse angle ∠GHI.
Given:
- ∠GHI = 135°
- ∠GHJ = 112°
Using the equation for adjacent angles, we have:
\[ ∠GHI = ∠GHJ + ∠JHI \]
Substituting the known values:
\[ 135° = 112° + ∠JHI \]
Now, we solve for ∠JHI:
\[ ∠JHI = 135° - 112° \] \[ ∠JHI = 23° \]
Thus, the measure of ∠JHI is 23°.
The correct answer is:
D. 23°