A chord of a circle is equal to the radius of the circle.

Solution:

We have,

Radius OA = Chord AB

⟹ OA = OB = AB

Then triangle OAB is an equilateral triangle.

∴ ∠AOB = 60° [one angle of equilateral triangle]

By degree measure theorem

∠AOB = 2∠APB

⇒ 60° = 2∠APB

⇒ ∠APB = 60°/2 = 30°

Now, ∠APB + ∠AQB = 180° [opposite angles of cyclic quadrilateral]

⇒ 300 + ∠AQB = 180°

⇒ ∠AQB = 180° − 30° = 150°.

Therefore, Angle by chord AB at minor arc = 150^°

Angle by chord AB at major arc = 30