A, B, C, D are four points on a circle. AC and BD intersect

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

1. 120°
2. 90°
3. 100°
4. 110°

Correct Option: D

According to question , we draw a figure of a circle ,

Given, ∠BEC = 130° and ∠ECD = 20°
⇒ ∠DEC = 180° – 130° = 50°
∴ ∠EDC = 180° – 50° – 20° = 110°
∴ ∠BAC = ∠EDC = 110°
(Angles on the same arc)