Triangle ABC-isosceles AB-base. The bisectors of the angles at the base intersect at point D.

Triangle ABC-isosceles AB-base. The bisectors of the angles at the base intersect at point D. Angle C is 100 degrees. Find the ADB angle.

The sum of the angles of a triangle is 180 degrees, the angles at the base of an isosceles triangle are equal, which means
angle A = angle B = (180-angle C) / 2 = (180-100) / 2 = 80/2 = 40 degrees. Consider a triangle ABD: AD and BD are bisectors, so the angle DAB = angle DBA = 40/2 = 20 degrees. Angle ADB = 180-angle DAB-angle DBA = 180-20-20 = 140 degrees.