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In the Given Figure, Ab = Bc = Cd and ∠Abc = 132 . Calcualte: - Mathematics

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Question

In the given figure, AB = BC = CD and ∠ABC = 132° . Calcualte: ∠AEB

Solution

In the figure, O is the centre of circle, with AB = BC = CD.
Also, ∠ABC = 132°

In cyclic quadrilateral ABCE
∠ABC + ∠AEC = 180°               [sum of opposite angles]
→ ∠132 + ∠AEC = 180°
→ ∠AEC = 180° -132°
→ ∠AEC = 48°

Since, AB = BC, ∠AEB = ∠BEC          [equal chords subtends equal angles]

∴ ∠AEB = `1 /2` ∠AEC
           = `1 /2xx 48° `
           = 24°

  Is there an error in this question or solution?
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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(B) | Q: 7.1 | Page no. 265
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In the Given Figure, Ab = Bc = Cd and ∠Abc = 132 . Calcualte: 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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