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April 2nd, 2011, 12:48 PM   #1
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determine angle B

Hello, I found this problem in a textbook






this is my attempt of solving it
a + b = 8c
and a + b + c = 360

substituting: 8c + c = 360

9c = 360

c = 40

but now I got stuck

the book says the answer is 20, but I just can't figure out how to get to the answer
I would really appreciate your help
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April 2nd, 2011, 10:30 PM   #2
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?BAC + ?ABC : ?ACB = 320 : 40 = 8 : 1
180 = 8x + x = 9x
x = 20
? ?BAC + ?ABC = 160
? ?ACB = 20
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April 3rd, 2011, 08:58 PM   #3
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Re: determine angle B

thank you for your help, although i cant fully understand the solution, i am not very good at math

could you give me a brief explanation please?
regards
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April 4th, 2011, 02:38 AM   #4
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We know that arc c is 40, hence arc a + arc b is 320 in order to make 360 rotation possible.
?ACB depends on arc c and ?BAC + ?ABC depends on arc a + arc b.
?ACB + ?BAC + ?ABC = 180 and 8?ACB = ?BAC + ?ABC, hence ?ACB + 8?ACB = 9?ACB = 180.
? ?ACB = 20, ?BAC + ?ABC = 160
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April 4th, 2011, 04:40 AM   #5
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The question asks for angle B, not C. You would need additional information to determine B.
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