In triangle ABC, angle A is 35 °, angle B is 20 °. AD, BE and CF – heights crossing at point O.

In triangle ABC, angle A is 35 °, angle B is 20 °. AD, BE and CF – heights crossing at point O. Find the AOF corner. Give your answer in degrees.

First way.
Since the angle С is obtuse, the heights of the triangle intersect on the continuation of the heights.
In a right-angled triangle ACF, define the value of the angle BCF.
Angle ACF = (180 – 90 – 20) = 700.
Angle OСD = ACF as vertical angles. OСD angle = 700.
Then in a right-angled triangle OСD the angle СOD = (180 – 90 – 70) = 200.

Second way.
Consider a right-angled triangle of the AВD, in which the angle of ADВ = (180 – 90 – 20) = 700.
The AFO triangle is rectangular, then the AOF angle = (180 – 90 – 70) = 200.
Answer: Angle AOF is 200.