SOLUTION: the three angles of a triangle are in a 1:2:3 ratio. What are their measurements?

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Question 157103: the three angles of a triangle are in a 1:2:3 ratio. What are their measurements?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
the three angles of a triangle are in a 1:2:3 ratio. What are their measurements?

Let the angles be A, B, and C

1 is to the sum 1%2B2%2B3 as A is to the sum A%2BB%2BC

1%2F%281%2B2%2B3%29=A%2F%28A%2BB%2BC%29

But since A%2BB%2BC=180°

1%2F%281%2B2%2B3%29=A%2F180

1%2F6=A%2F180

Cross-multiply:

6A=180

Divide both sides by 6

A=30°

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2 is to the sum 1%2B2%2B3 as B is to the sum A%2BB%2BC

2%2F%281%2B2%2B3%29=B%2F%28A%2BB%2BC%29

But since A%2BB%2BC=180°

2%2F%281%2B2%2B3%29=B%2F180

2%2F6=B%2F180

Cross-multiply:

6B=360

Divide both sides by 6

B=60°

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To find the third angle you could just add those
two and subtract from 180°, but as a check you
could do it like the others:

3 is to the sum 1%2B2%2B3 as C is to the sum A%2BB%2BC

3%2F%281%2B2%2B3%29=C%2F%28A%2BB%2BC%29

But since A%2BB%2BC=180°

3%2F%281%2B2%2B3%29=C%2F180

3%2F6=C%2F180

Cross-multiply:

6C=540

Divide both sides by 6

C=90°

Edwin