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)

A. 68°

B. 15°

C. 90°

D. 23°

1 answer

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°