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Measure that angle II (Posted on 2004-09-01) Difficulty: 2 of 5
Triangle ABC is isosceles with AB=BC. There is a point D on AC such that BD = DC and AB=AD.

What is the measure of angle BAC?

  Submitted by Brian Smith    
Rating: 2.6667 (3 votes)
Solution: (Hide)
Let angle BAC = x
Since ABC is isosceles:
angle BCA = x
angle ABC = 180-2x

BDC is isosceles since BD=DB, then:
angle DBC = x
angle BDC = 180-2x
angle ADB = 2x
angle ABD = 180-3x

BAD is isosceles since BA=AD, then:
angle ADB = angle ABD
2x = 180-3x
x = 36

Angle BAC = 36 degrees

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionExplanation to Puzzle AnswerK Sengupta2022-05-23 22:07:15
Some Thoughtsre: Independent solutionK Sengupta2022-05-21 23:43:11
answerK Sengupta2007-06-19 06:08:34
re(2): More than you think!Jim2004-09-13 14:52:34
re: More than you think!Jim2004-09-13 14:44:22
SolutionMore than you think!Jim2004-09-13 14:38:35
re(4): Solution + Explanationnikki2004-09-02 08:15:18
re: Independent solutionBruce Brantley2004-09-02 00:26:23
SolutionIndependent solutionTristan2004-09-01 17:36:08
re(3): Solution + ExplanationCharlie2004-09-01 16:39:30
SolutionConcise SolutionRichard2004-09-01 14:14:34
SolutionSimpleOskar2004-09-01 09:57:08
re(3): Solution + Explanationnikki2004-09-01 09:35:45
re(2): Solution + Explanationnikki2004-09-01 09:34:43
re(2): Solution + ExplanationSyzygy2004-09-01 09:31:15
SolutionPure Algebra for GeometrySyzygy2004-09-01 09:21:54
Solutionre: Solution + ExplanationCharlie2004-09-01 08:43:45
SolutionSolution + Explanationnikki2004-09-01 08:31:31
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