An obtuse ∠GHI is 135°. It contains adjacent angles GHJ and JHI. ∠GHJ is 112°. What is the measure of ∠JHI
To find the measure of ∠JHI, we first need to find the measure of ∠GHI.
Given that ∠GHI is an obtuse angle and its measure is 135°, we know that the measure of ∠GHI is greater than 90° but less than 180°.
Next, we are given that ∠GHI contains adjacent angles GHJ and JHI. Since adjacent angles form a straight line, the sum of their measures equals 180°.
The measure of ∠GHJ is given as 112°.
To find the measure of ∠JHI, we can subtract the known measure of ∠GHJ from the measure of ∠GHI:
∠GHI - ∠GHJ = ∠JHI
Substituting the values, we have:
135° - 112° = ∠JHI
Simplifying, we get:
23° = ∠JHI
Therefore, the measure of ∠JHI is 23°.
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To find the measure of ∠JHI, we can use the fact that the sum of the measures of angles around a point is always 360 degrees.
First, we know that ∠GHI is an obtuse angle and measures 135 degrees.
Next, we have ∠GHJ, which measures 112 degrees.
To find ∠JHI, we need to subtract the sum of ∠GHI and ∠GHJ from 360 degrees.
So, ∠JHI = 360° - ∠GHI - ∠GHJ
Substituting the given values, we get:
∠JHI = 360° - 135° - 112°
∠JHI = 113°
Therefore, the measure of ∠JHI is 113 degrees.