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In the Given Figure, Aoc is a Diameter and Ac is Parallel to Ed. If ∠Cbe = 64°, Calculate ∠Dec . - Mathematics

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Question

In the given figure, AOC is a diameter and AC is parallel to ED. If ∠CBE = 64°, Calculate ∠DEC .

Solution

Join AB,
∠ABC = 90°
(Angle in a semi circle)
∴ ∠ABE = 90° - 64° = 26°

Now, ∠ABE = ∠ACE = 26°

(Angle in the same segment)

Also, AC || ED
∴ ∠DEC = ∠ACE = 26°     (Alternate angles)

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(A) | Q: 46 | Page no. 261
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In the Given Figure, Aoc is a Diameter and Ac is Parallel to Ed. If ∠Cbe = 64°, Calculate ∠Dec . Concept: Arc and Chord Properties - Angles in the Same Segment of a Circle Are Equal (Without Proof).
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