SOLUTION: One angle of a triangle exceeds another by 23 degrees. the third is 6 degrees less than the sum of the others. FInd the measures of the angles.
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Question 71305: One angle of a triangle exceeds another by 23 degrees. the third is 6 degrees less than the sum of the others. FInd the measures of the angles. Answer by 303795(602) (Show Source):
You can put this solution on YOUR website! Call the second angle x. The first angle must therefore be (x + 23). The third angle is 6 less than (x + x + 23) ie the third angle is (2x + 17).
The three angles in a triangle add up to 180 degrees so
x + (x + 23) + (2x + 17) = 180
4x + 40 = 180
4x = 140
x = 35 degrees
The first angle is (x + 23) = 35 + 23 = 58 degrees
The third angle is (2x + 17) = 2*35 + 17 = 70 + 17 = 87 degrees
So the angles are 35, 58 and 87 degrees.
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