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
?(1 point)
Responses

23°
23 degrees

15°
15 degrees

90°
90 degrees

68°

1 answer

To find the measure of angle \( \angle JHI \), we can use the fact that the sum of adjacent angles that form a straight line (or are on a straight angle) equals 180°.

We know:

  • \( \angle GHI = 135° \)
  • \( \angle GHJ = 112° \)

To find \( \angle JHI \), we can use the relationship:

\[ \angle GHI = \angle GHJ + \angle JHI \]

Substituting the known values:

\[ 135° = 112° + \angle JHI \]

Now, subtract \( 112° \) from both sides:

\[ \angle JHI = 135° - 112° = 23° \]

Thus, the measure of \( \angle JHI \) is \( 23° \).

The correct response is:

23°