In triangle ABC, angle A = 72 °, angle B = 91 °. point K lies on the continuation of the AC side, find the angle BCK.

First way.

Determine the value of the angle ACB in the triangle ABC.

The sum of the inner angles of the triangle is 180, then the angle ACB = (180 – ABC – CAB) = (180 – 91 – 72) = 17.

The sought angle ВСК and the angle AСB are adjacent angles, the sum of which is 1800, then the angle ВСК = (180 – AСB) = (180 – 17) = 163.

Second way.

The angle ВСК is the outer angle of the triangle ABC at the vertex C, then its value is equal to the sum of two inner angles of the triangle that are not adjacent to it. ВСK angle = (ABC + CAB) = (91 + 72) = 163.

Answer: The ВСК angle is 163.