In triangle ABC, angle A = 54 degrees Find the larger of the angles between the bisectors of angles B and C.
| May 30, 2021 | education
The sum of the inner angles of the triangle is 180, then the sum of the angles (ABC + ABC) = (180 – BAC) = (180 – 54) = 126.
Since BM and CК are bisectors of the angles, then the angle ОВС = ABC / 2, the angle OCB = АСВ / 2.
Then the sum of the angles (OBC + OCB) = (ABC + ACB) / 2 = 126/2 = 63.
Then the angle BОС = 180 – 63 = 117.
Answer: The larger angle between the bisectors is 117.
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