Question 1100103: ABC is a triangle with 35 times the smallest angle is equal to 27 times the largest angle. What is the measure of second largest angle?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Let S = the smallest angle
Let L = the largest angle
Let M = the middle angle
35S = 27L -> L = 35/27S
The three angles add up to 180:
S + 35/27S + M = 180
M = 180 - S - 35/27S = (62/27)S
If we assume the angles must be whole numbers, then S must be multiples of the
denominator, 27.
If A = 27, this would give M = 118, but the middle angle must be less than 90
If A = 54, this gives M = 56
If A = 81, this gives M = -6, which is impossible
Thus the only candidate is A = 54
Therefore the three angles are 54, 56 and 70
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