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