My Math Forum determine angle B

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 April 2nd, 2011, 12:48 PM #1 Newbie   Joined: Apr 2011 Posts: 2 Thanks: 0 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 20º, but I just can't figure out how to get to the answer I would really appreciate your help
 April 2nd, 2011, 10:30 PM #2 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 ?BAC + ?ABC : ?ACB = 320 : 40 = 8 : 1 180° = 8x + x = 9x x = 20° ? ?BAC + ?ABC = 160° ? ?ACB = 20°
 April 3rd, 2011, 08:58 PM #3 Newbie   Joined: Apr 2011 Posts: 2 Thanks: 0 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
 April 4th, 2011, 02:38 AM #4 Senior Member   Joined: Apr 2007 Posts: 2,140 Thanks: 0 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°
 April 4th, 2011, 04:40 AM #5 Global Moderator   Joined: Dec 2006 Posts: 19,162 Thanks: 1638 The question asks for angle B, not C. You would need additional information to determine B.

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