To find the measure of angle \( \angle JHI \), we can use the fact that adjacent angles \( \angle GHI \) and \( \angle GHJ \) add up to \( \angle GHI \).
Given:
- \( \angle GHI = 135^\circ \)
- \( \angle GHJ = 112^\circ \)
Now, we use the following relationship:
\[ \angle GHI = \angle GHJ + \angle JHI \]
Substituting the known values:
\[ 135^\circ = 112^\circ + \angle JHI \]
Now, we can solve for \( \angle JHI \):
\[ \angle JHI = 135^\circ - 112^\circ = 23^\circ \]
Thus, the measure of \( \angle JHI \) is \( 23^\circ \).
The correct response is \( \boxed{23^\circ} \).