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In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC - CBSE Class 9 - Mathematics

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Question

In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

Solution

In ΔCDE,

∠CDE + ∠DCE = ∠CEB (Exterior angle)

⇒ ∠CDE + 20° = 130°

⇒ ∠CDE = 110°

However, ∠BAC = ∠CDE (Angles in the same segment of a circle)

⇒ ∠BAC = 110°

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 10: Circles
Ex. 10.50 | Q: 5 | Page no. 185

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Solution In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC Concept: Cyclic Quadrilaterals.
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