In triangle ABC, angle A is 60 ° and angle B is 82 °. AD, BE, CF-heights intersecting at point O. find the angle AOF.

Consider a triangle ABD: the angle ABD is 82 °, the angle BDA is 90 ° (since AD is the height). find the angle BAD (the sum of the angles in the triangle is 180 °):

DAB = 180 ° – (ABD + BDA) = 180 ° – (82 ° + 90 °) = 180 ° – 172 ° = 8 °.

Consider a triangle AOF: the OFA angle is 90 °, the OAF angle = DAB angle = 8 °.

Let’s calculate the value of the angle AOF (the sum of the angles is equal to 180 °):

AOF = 180 ° – (OAF + OFA) = 180 ° – (8 ° + 90 °) = 180 ° – 98 ° = 82 °.

Answer: The AOF is 82 °.