Let BD bisect angle ABC in triangle ABC. Given angle ABC = 60 degrees and AB = BC + CD, find angle BAC.

Bridger Holden 2022-09-29 Answered
Let BD bisect A B C in Δ A B C. Given A B C = 60 degrees and A B = B C + C D, find B A C
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Answers (1)

Alannah Hanson
Answered 2022-09-30 Author has 11 answers
Step 1

Construct the point E on AB such that E B = B C. Then A E = B A B E = B A B C = C D.
Besides B E D B C D by SAS. Hence E D = C D = A E.
Step 2
We have E A D = E D A = α. E D B = C D B = 1 2 ( 180 α ).
We also have B E D = 2 α. Now considering the interior angles of B E D, 30 + 2 α + 1 2 ( 180 α ) = 180 .
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