In the given figure, and are straight lines through the center of a circle. If and find (i) (ii)

Question

Philoid · Accepted Answer

(i)

In triangle CDE,

∠CDE + ∠CED + ∠DCE = 180°[Sum of angles of triangle]

⇒ 40° + 90° + ∠DCE = 180°

⇒ 130° + ∠DCE = 180°

⇒ ∠DCE = 50°

(ii)

∠AOC + ∠BOC = 180°[Because AOB is a straight line]

⇒ 80° + ∠BOC = 180°

⇒ ∠BOC = 100°

In triangle BOC,

∠OCB + ∠BOC + ∠OBC = 180°[Sum of angles of triangle]

⇒ 50° + 100° + ∠OBC = 180°[∠DCE = 50°]

⇒ 150° + ∠OBC = 180°

⇒ ∠OBC = 30°

∴ ∠ABC = ∠OBC = 30°