In the adjoining figure, is the center of a circle, and find

Question

Philoid · Accepted Answer

∠DCB = (1/2) ∠AOB [∠DCB = ∠ACB]

⇒ ∠DCB = (1/2) 40°

⇒ ∠DCB = 20°

In triangle BCD,

∠BDC + ∠DCB + ∠DBC = 180°[Sum of angles of triangle]

⇒ 100° + 20° + ∠OBC = 180°

⇒ 120° + ∠DBC = 180°

⇒ ∠DBC = 60°

∴ ∠OBC = ∠DBC = 60°