#### Question

In the figure given below, AB and CD are straight lines through the centre O of a circle. If ∠AOC

= 80° and ∠CDE = 40°, Find the number of degrees in:

(i) ∠ DCE, (ii) ∠ABC.

#### Solution

(i) Here, ∠CED =90°

(Angle in a semicircle is a right angle)

∴ ∠DCE = 90° - ∠CDE = 90° - 40° = 50°

∴ ∠DCE = ∠OCB =50°

(ii) In ΔBOC,

∠AOC = ∠OCB + ∠OBC

(Exterior angle of a Δ is equal to the sum of pair of interior opposite angles)

⇒ ∠OBC = 80° - 50° = 30° [ ∠AOC = 80° ,given ]

Hence, ∠ABC = 30°

Is there an error in this question or solution?

Solution In the Figure Given Below, Ab and Cd Are Straight Lines Through the Centre O of a Circle. If ∠Aoc = 80° and ∠Cde = 40°, Find the Number of Degrees In: (I) ∠ Dce, (Ii) ∠Abc. Concept: Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse.