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 ?
The sum of the measures of angles in a triangle is 180 degrees. Therefore, ∠GHI + ∠GHJ + ∠JHI = 180°.
Substituting the given values, we have 135° + 112° + ∠JHI = 180°.
Combining like terms, we have 247° + ∠JHI = 180°.
Subtracting 247° from both sides, we have ∠JHI = 180° - 247°.
Simplifying, we have ∠JHI = -67°.
Since angles cannot have negative measures, there is no solution for ∠JHI in this case.