Question

In the figure given alongside, 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:

1. ∠DCE,
2. ∠ABC.

Answer 1

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)

${\displaystyle \Rightarrow }$ ∠OBC = 80° – 50° = 30°  ...[∠AOC = 80°, given]

Hence, ∠ABC = 30°