SOLUTION: The measure of an obtuse angle is 24 less than three times the measure of its supplement. Find the measure of the angle.

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Question 125887: The measure of an obtuse angle is 24 less than three times the measure of its supplement. Find the measure of the angle.
Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!
- Obtuse angles are those angles which measure greater than 90 degrees but less than 180 degrees. Therefore our answer should fall between 90 and 180.
- Supplementary angles are two or more angles whose sum is 180 degrees.
Let X = Supplement to the angle we are looking for
Let 3x - 24 = The angle we are looking for (24 less than 3 times the measure of its supplement)

Solve:
1. Set up the equation:
x + (3x - 24) = 180
2. Combine the x terms:
4x - 24 = 180
3. Add 24 to both sides
4x = 204
4. Divide both sides by 4
x = 51
5. Substite:
3(51) - 24 = 153 - 24 = 129 degrees
Since our result is greater than 90 and less 180 it qualifies as an obtuse angle.
Note: You could also have subtracted 51 from 180 and achieved the same result.
180 - 51 = 129