SOLUTION: the second angle in a triangle is one-third as large as the first. the third angle is two-thirds as large as the first angle. find the measures

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Question 1151396: the second angle in a triangle is one-third as large as the first. the third angle is two-thirds as large as the first angle. find the measures
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = first angle
Let B = second angle
let C = third angle
the second angle in a triangle is one-third as large as the first.
 
B+=+expr%281%2F3%29A
the third angle is two-thirds as large as the first angle.
 
C+=+expr%282%2F3%29A
find the measures
They are the three angles of a triangle, so their sum is 180°.

A+%2B+B+%2B+C+=+180%5Eo

Substitute for B and C

A+%2B+expr%281%2F3%29A+%2B+expr%282%2F3%29A+=+180%5Eo

Multiply through ever term by 3

3A+%2B+A+%2B+2A+=+540%5Eo

6A=540%5Eo

A=90%5Eo

B+=+expr%281%2F3%29A
B+=+expr%281%2F3%2990%5Eo
B+=+30%5Eo

C+=+expr%282%2F3%29A
C+=+expr%282%2F3%2990%5Eo
C+=+60%5Eo

It's a 30°-60°-90° right triangle

Edwin