SOLUTION: One angle of a triangle is 3 times as large as another. The measure of the third angle is 40 degrees greater than that of the smallest angle. How large are the angles?

Question 743699: One angle of a triangle is 3 times as large as another. The measure of the third angle is 40 degrees greater than that of the smallest angle. How large are the angles?
Found 2 solutions by stanbon, davethejackal:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One angle of a triangle is 3 times as large as another. The measure of the third angle is 40 degrees greater than that of the smallest angle. How large are the angles?
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Equations:
a = 3b
c = b+40
a + b + c = 180
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Substitute for a and for c, and solve for "b":
3b + b + b+40 = 180
5b = 140
b = 28 degrees
a = 3b = 84 degrees
c = 68 degrees
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Cheers,
Stan H.
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Answer by davethejackal(28) (Show Source): You can put this solution on YOUR website!
Let , and be the angles in the triangle

Total angles in a triangle always add up to 180 so
[1]

"One angle of a triangle is 3 times as large as another"
[2]

"The measure of the third angle is 40 degrees greater than that of the smallest angle"
[3]

substituting for in [1] using [2] and [3] gives

hence

or

Using [3] gives

Checking in [1]
a[1], a[2], a[3] = 84 + 68 + 28 = 180 QED
The 3 angles are 28, 68 and 84 degrees.
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