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Measure that angle III (Posted on 2004-09-07) Difficulty: 4 of 5
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

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-06-19 06:09:44
re(2): Got it!Ken Haley2004-09-15 00:26:26
re: Got it!nikki2004-09-13 15:55:52
Link (spoilers for sure)Richard2004-09-10 19:26:57
SolutionGot it!Ken Haley2004-09-10 00:41:30
No SubjectKen Haley2004-09-09 23:31:05
re(2): first partnikki2004-09-09 17:11:54
QuestionI just noticed.....Jim2004-09-09 14:58:27
Solutionre: first partJim2004-09-09 14:31:31
Some Thoughtsfirst partJim2004-09-09 14:15:38
Some ThoughtsAlmost solutions without cheating (could be considered a spoiler)nikki2004-09-09 08:26:55
re(3): Solution by cheatingnikki2004-09-09 08:26:03
re(2): Solution by cheatingKen Haley2004-09-08 23:12:16
re: Solution by cheatingBrian Smith2004-09-08 15:28:57
re: Solution by cheatingJuggler2004-09-08 13:44:48
re: Solution by cheatingRichard2004-09-08 13:32:10
SolutionSolution by cheatingnikki2004-09-08 12:44:58
Best I could doJer2004-09-08 12:40:50
Trig to Non-Trig?Richard2004-09-08 12:37:36
Some Thoughtsre: Silly guessSyzygy2004-09-08 08:35:19
Silly guessLarry2004-09-08 07:45:17
On a possible way to a solution perhaps...Mike Graham2004-09-08 02:06:54
Ways to solveGamer2004-09-07 22:58:38
re: Mmmm. An answer, Maybe,Mike Graham2004-09-07 20:19:35
SolutionMmmm. An answer, Maybe,Juggler2004-09-07 19:17:00
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