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Question 157103: the three angles of a triangle are in a 1:2:3 ratio. What are their measurements?: the three angles of a triangle are in a 1:2:3 ratio. What are their measurements?
Answer by Edwin McCravy(2086) 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+2+3 as A is to the sum A+B+C

1/(1+2+3)=A/(A+B+C)

But since A+B+C=180°

1/(1+2+3)=A/180

1/6=A/180

Cross-multiply:

6A=180

Divide both sides by 6

A=30°

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2 is to the sum 1+2+3 as B is to the sum A+B+C

2/(1+2+3)=B/(A+B+C)

But since A+B+C=180°

2/(1+2+3)=B/180

2/6=B/180

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+2+3 as C is to the sum A+B+C

3/(1+2+3)=C/(A+B+C)

But since A+B+C=180°

3/(1+2+3)=C/180

3/6=C/180

Cross-multiply:

6C=540

Divide both sides by 6

C=90°

Edwin