In triangle ABC the angle at B is 80° and the angle at C is 40°. The bisector of angle A meets BC at the point D. What is the measure of angle ADB?

The angle at A is 180° − 80° − 40° = 60°, so the bisector gives angle BAD = 30°. In triangle ABD, angle ADB = 180° − 80° − 30° = 70°. The trap 110° is angle ADC, the other angle on the straight line BC, and indeed 180° − 40° − 30° = 110°.