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In the Figure, O is the Centre of the Circle, ∠Aoe = 150°, ∠Dao = 51°. Calculate the Sizes of the Angles Ceb and Oce. - ICSE Class 10 - Mathematics

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ConceptArc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle

Question

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

Solution

∠ADE = `1/2`Re flex (∠AOE) = `1/2` (360° -150° ) = 105° 

(Angle at the center is double the angle ate 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° 

  Is there an error in this question or solution?
Solution In the Figure, O is the Centre of the Circle, ∠Aoe = 150°, ∠Dao = 51°. Calculate the Sizes of the Angles Ceb and Oce. Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.
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