Question

A designer creates a circular ornament as shown. Identify m∠ADB.

.__. I keep getting confused with this question.

The answers are:

m∠ADB = 110°

m∠ADB = 100°

m∠ADB = 105°

or

m∠ADB = 95°

Answer 1

Shown on the diagram, for me, the angle of 120° is not actually like an acute angle (because 120° is an obtuse angle). Once you divide it by 2, you'll get 60 deg which is considered an acute angle. The ∠BAC is also 60°. Notice that combining ∠ABD, ∠BAD and ∠ADB forms a triangle. Since the total angle of a triangle is always 180°. You can solve for ∠ADB as:
∠ABD + ∠BAD + ∠ADB = 180°
25° + 60° + ∠ADB = 180°
∠ADB = 95°