To find the measure of angle \( \angle JHI \), we can use the fact that the sum of the measures of adjacent angles in a straight line is equal to the measure of the obtuse angle \( \angle GHI \).
We know the following:
- \( \angle GHI = 135^\circ \)
- \( \angle GHJ = 112^\circ \)
- Let \( \angle JHI = x \) (the angle we want to find)
Since \( \angle GHJ \) and \( \angle JHI \) are adjacent to the obtuse angle \( \angle GHI \), we have:
\[ \angle GHI = \angle GHJ + \angle JHI \]
Substituting the known values:
\[ 135^\circ = 112^\circ + x \]
To find \( x \), we can rearrange the equation:
\[ x = 135^\circ - 112^\circ \] \[ x = 23^\circ \]
Thus, the measure of \( \angle JHI \) is \( 23^\circ \).
The correct response is:
23°
1 answer