In triangle ABC, angle B is 20. bisectors AA1 and CC1 intersect at point O. Find angle ACO.
| May 25, 2021 | education
The sum of the inner angles of the triangle is 180, then the sum of the angles (BAC + BCA) = (180 – ABC) = (180 – 20) = 160.
Since AA1 and CC1 are the bisectors of the angles, the angle BAA1 = CAA1 = BAC / 2, the angle BCC1 = ACC1 = BCA / 2.
The sum of the angles (OAС + OCA) = (BAC / 2 + BCA / 2) = (BCA + BAC) / 2 = 160/2 = 80.
Then, in the AOC triangle, the AOC angle = (180 – (OAC + OCA)) = (180 – 80) = 100.
Answer: The AOC angle is 100.
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