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 Measure that angle III (Posted on 2004-09-07)
Triangle ABC has side AB=AC, and angle BAC = 20 degrees.

D is a point on side AC with AD=BC. Find angle DBC.

Solve this without trigonometry.

 Submitted by Brian Smith Rating: 3.2000 (5 votes) Solution: (Hide) Given: AB=AC, BAC=20, AD=BC, ABC is isosceles. Find the point E such that EA = ED = AB, with E and B both on the same side of line ADC. Then: triangles AED and BAC are congruent triangle EAB is isosceles angle AED = 20 angle EAD = 80 angle EAB = 60 triangle EAB is equilateral angle AEB = 60 angle DEB = 40 EA=EB=ED triangle DEB is isosceles angle DBE = angle BDE = 70 angle EBA = 60 angle EBC = 140 angle DBC = 70 degrees

 Subject Author Date answer K Sengupta 2007-06-19 06:09:44 re(2): Got it! Ken Haley 2004-09-15 00:26:26 re: Got it! nikki 2004-09-13 15:55:52 Link (spoilers for sure) Richard 2004-09-10 19:26:57 Got it! Ken Haley 2004-09-10 00:41:30 No Subject Ken Haley 2004-09-09 23:31:05 re(2): first part nikki 2004-09-09 17:11:54 I just noticed..... Jim 2004-09-09 14:58:27 re: first part Jim 2004-09-09 14:31:31 first part Jim 2004-09-09 14:15:38 Almost solutions without cheating (could be considered a spoiler) nikki 2004-09-09 08:26:55 re(3): Solution by cheating nikki 2004-09-09 08:26:03 re(2): Solution by cheating Ken Haley 2004-09-08 23:12:16 re: Solution by cheating Brian Smith 2004-09-08 15:28:57 re: Solution by cheating Juggler 2004-09-08 13:44:48 re: Solution by cheating Richard 2004-09-08 13:32:10 Solution by cheating nikki 2004-09-08 12:44:58 Best I could do Jer 2004-09-08 12:40:50 Trig to Non-Trig? Richard 2004-09-08 12:37:36 re: Silly guess Syzygy 2004-09-08 08:35:19 Silly guess Larry 2004-09-08 07:45:17 On a possible way to a solution perhaps... Mike Graham 2004-09-08 02:06:54 Ways to solve Gamer 2004-09-07 22:58:38 re: Mmmm. An answer, Maybe, Mike Graham 2004-09-07 20:19:35 Mmmm. An answer, Maybe, Juggler 2004-09-07 19:17:00

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