The point K is taken inside the triangle ABC so that the angle ABK = 30, KAB = 10.

The point K is taken inside the triangle ABC so that the angle ABK = 30, KAB = 10. Find the angle KAC if ABC = 80 and AC = BC.

AC = BC, which means triangle ABC is isosceles and angle ABC = angle BAC = 80 (as angles at the base of an isosceles triangle).

Let’s draw the segments AK and BK. In the triangle ABK, the angle KAB = 10. the angle BAC is equal to the sum of the angles BAC and KAC, then the angle KAC = 80 – 10 = 70.

Answer: 70