In triangle ABC. AB = BC, angle B = 80 degrees. The bisectors of angles A and C meet at point M. Find the angle AMC.

Since AB = BC, the triangle ABC is isosceles, which means the angles A and C at the base of AC are equal to each other. Because angle B = 80, then angle A = angle C = (180-angle B) / 2 = (180-80) / 2 = 50 degrees. The bisectors of angles A and C divide them in half, which means that in the AMC triangle the angles MAC and MCA are equal and amount to 50/2 = 25 degrees. The AMC angle is 180-25-25 = 130 degrees.