Question 243712: If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! This problem hinges on your remembering that the sum of the angles in a triangle is always 180.
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In this case we have 3 unknown angles: a, b, and c.
However, we are told they have a specific relationship: 1 to 3 to 5. So the second angle is 3 times the first and the third angle is 5 times the first.
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a = a
b = 3a
c = 5a
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a + b + c = 180
Substituting,
a + 3a + 5a = 180
9a = 180
Divide both sides by 9
a = 20
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Substituting back into the formulas we defined.
a = 20
b = 3a = 3(20) = 60
c = 5a = 5(20) = 100
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Check the work.
Does 20 + 60 + 100 = 180?
Yes.
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Done.
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