ABC is a triangle in which angle B= 2 angle C. D is a point on BC such that AD bisects angle BAC and AB=CD. Prove that angle BAC=72°

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21-11-2016
Mathematics

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ABC is a triangle in which angle B= 2 angle C. D is a point on BC such that AD bisects angle BAC and AB=CD. Prove that angle BAC=72°

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syed514 syed514 · Answer 1 · 2016-11-21T19:54:26+01:00

syed514 syed514

21-11-2016

so Triangle ABC and ADC are similar (two sides and one angle is equal)so angle CAD = angle ACB =cso angle BAC=2cand in triangle ABCangle BAC + angle ABC + angle ACB = 2c+2c+c = 5c = 180c=180/5 = 36angle BAC =2c=2*36 =72

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