The bissictrix of angle A of triangle ABC intersects side AC at point K. Point N is marked on side AB so that AN = NK.

The bissictrix of angle A of triangle ABC intersects side AC at point K. Point N is marked on side AB so that AN = NK. Find the angles of triangle ANK if the angle ABC = 40 degrees and the angle BAC-angle ABC = 20 degrees.

Let’s designate the angle BAC = X0, then, according to the condition, the angle ACB = X – 20.

Then the sum of the interior angles of the triangle ABC will be equal to 1800, then 180 = 40 + X + X – 20.

2 * X = 160.

BAC = X = 80.

ASV = 80 – 20 = 60.

AK is the bisector of angle A, then the angle BAK = 80/2 = 40.

AK = NK by condition, then AKN is an isosceles triangle, which means the angle ANK = NAK = 40.

Angle ABN = 180 – 40 – 40 = 100.

Answer: The angles of triangle АNК are equal to 100, 40, 40.