In an isosceles triangle ABC with a base AC and an apex angle B equal to 80 degrees

In an isosceles triangle ABC with a base AC and an apex angle B equal to 80 degrees, an AK bisector was drawn. Find the angle CAK.

Since the triangle ABC is isosceles, the angle BAC = BCA = (180 – ABC) / 2 = (180 – 80) / 2 = 50.

The segment AK is the bisector of the angle BAC, then the angle BAC = CAK = BAC / 2 = 50/2 = 25.

The sum of the interior angles of the triangle is 180, then in the CAK triangle the angle AKC = (180 – AСK – CAK) = (180 – 50 – 25) = 105.

Answer: The angles of the CAK triangle are 25, 50, 105.