The bisectors of angles A and B of an equilateral triangle ABC meet at point O. Find the angle AOB.
| April 21, 2021 | education
Since the triangle is equilateral, all of its angles are 60. Angle BAC = BCA = ABC = 60.
AA1 is the bisector of the angle BAC, then the angle OAB = 60/2 = 30.
BB1 is the bisector of the angle ABC, then the angle ABO = 60/2 = 30.
Then the angle AOB = 180 – OAB – ABO = 180 – 30 – 30 = 120.
Answer: Angle AOB is 120.
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