SOLUTION: in triangle abc, angle b is 40 degrees less than angle a and angle c is two times bigger than angle b. What is the measure of each angle?

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Question 1114392: in triangle abc, angle b is 40 degrees less than angle a and angle c is two times bigger than angle b. What is the measure of each angle?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
system%28b=a-40%2Cc=b%2B2b%2Ca%2Bb%2Bc=180%29


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angle c is two times bigger than angle b.
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That is like, if c is p times bigger than b, then c=b+p.
Best to try avoid confusing with, "if c is p times as big as b, then c=p*b.


system%28a=b%2B40%2Cc=3b%2Ca%2Bb%2Bc=180%29
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In a one-variable equation,
%28b%2B40%29%2Bb%2B%283b%29=180
.
.
5b=140
highlight%28b=28%29
and use this to find a and c.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor is correct. The phrase "angle c is two times bigger than angle b", correctly interpreted, means that c is equal to b plus two more times b: c = b+2b = 3b.

When the problem is finished with that interpretation, the angles are b=28, a=b+40 = 68, and c=3b = 84.

It is very likely that the author of the problem meant that angle c is two times AS BIG AS angle b; that would mean c = 2b.

Of course you get different answers to the problem with the different interpretations. With the grammatically incorrect interpretation that c=2b, the angles are b=35, a=35+40=75, and c=2b=70.