Triangle ABC is isosceles with the base of the AC, angle С = 50 °, BО – height. Determine the angles of the ABO triangle

In order to find the angles at the base of an isosceles triangle, we start by using the property of angles at the base of an isosceles triangle – they are equal to each other. In our case, angle A = angle C = 50 °.

It is known that the height BO is lowered to the base of AC and hence the angle BOA = 90 °.

And we just have to find the degree measure of the angle ABO, we apply the theorem on the sum of the angles of a triangle. It says that the sum of the angles of a triangle is 180 °.

We know the degree measure of two angles, so we can find the third one like this:

ABO angle = 180 ° – (BAO angle + BOA angle) = 180 ° – (50 ° + 90 °) = 180 ° – 140 ° = 40 °.