SOLUTION: In a triangle, the largest angle is 100° greater than the smallest angle. The largest angle is 3 times as large as the third angle. Find the measure of each angle.

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Question 1203158: In a triangle, the largest angle is 100° greater than the smallest angle. The largest angle is 3 times as large as the third angle. Find the measure of each angle.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
smallest            c
largest            c+100
third angle       (1/3)(c+100)
SUM                180

That is exactly as described, except that a separate variable was not assigned for "the third angle".
Also notice as expressed, largest IS three times the size of the "third" side.
.
.
RESULTS
smallest     20
largest     120
the third    40

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
In a triangle, the largest angle is 100° greater than the smallest angle. The largest angle is 3 times as large as the third angle. Find the measure of each angle.

Let the measure of the MIDDLE angle be M
Then measure of largest angle  = 3M
And, measure of smallest angle = 3M - 100
As all interior angles of a triangle sum to 180, we get: M + 3M + 3M - 100 = 180
7M = 180 + 100

Find M, the measure of the middle angle, then substitute that value to find the largest and smallest angles. FINITO!!
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