Question

In the figure, O is the centre of the circle, ∠AOE = 150°, ∠DAO = 51°. Calculate the sizes of the angles CEB and OCE.

Answer 1

∠ADE = `1/2` Reflex (∠AOE)

= `1/2 (360^circ - 150^circ)`

= 105° 

(Angle at the center is double the angle at the circumference subtended by the same chord)

∠DAB + ∠BED = 180°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

`=>` ∠BED = 180° – 51° = 129° 

∴ ∠CEB = 180° – ∠BED  (Straight line)

= 180° – 129°

= 51°

Also, by angle sum property of ∆ADC,

∠OCE = 180° – 51° – 105° = 24°