What is my value ?

Geometry Level 2

If the angle A, B and C of triangle ABC satisfy the relation B - A = C - B, then what is the measure of angle B?


The answer is 60.

Neha Aggarwal by Neha Aggarwal , 21, India

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2 solutions

Noel Lo
Jul 21, 2017

B − A = C − B B-A=C-B

( 1 + 1 ) B = A + C (1+1)B=A+C

2 B = A + C 2B=A+C

A + B + C = 180 A+B+C=180

2 B + B = 180 2B+B=180

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

3 B = 180 3B=180

B = 60 B=60

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Casey McNamara
Jul 22, 2014

The three angles of a triangle must add up to 180 degrees. Because I only have one box into which to put an answer, I will assume that B, C, and A all have the same measure. Therefore that measure must be 60.

Seriously, though, the relation in the problem isn't a sufficient constraint. We can solve for B:

B - A = C - B

2B = A + C

and A + B + C = 180, so A + C = 180 - B

2B = 180 - B

3B = 180 and B = 60.

But that leaves A and C to be any two numbers that add up to 120. They could be both 60:

60 - 60 = 60 - 60 = 0

They could be 100 and 20:

60 - 100 = 20 - 60 = -40

They could be 1 and 119:

60 - 1 = 119 - 60 = 59

I would suggest editing the problem to only ask for the measure of angle B.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks, I've updated the question accordingly.

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Calvin Lin Staff - 6 years, 9 months ago

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