SOLUTION: The measure of one angle of a triangle is three times the measure of the smallest angle, and the measure of the last angle is equal to the sum of the other two angles. Find the me

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Question 339367: The measure of one angle of a triangle is three times the measure of the smallest angle, and the measure of the last angle is equal to the sum of the other two angles. Find the measure of the greatest angle of the triangle.
Answer by stanbon(75887) About Me  (Show Source):
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The measure of one angle of a triangle is three times the measure of the smallest angle, and the measure of the last angle is equal to the sum of the other two angles. Find the measure of the greatest angle of the triangle.
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Let "z" be the smallest angle:
x = 3z
y = x+z
x+y+z = 180
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Substitute and solve for "x":
x + (x+z) + (1/3)x = 180
x + x + (1/3)x + (1/3)x = 180
2x + (2/3)x = 180
6x + 2x = 540
8x = 540
x = 67.5 degrees
z = 67.5/3 = 22.5 degrees
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y = x+z = 90 degrees
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Cheers,
Stan H.