In figure, $A, B, C$ and $D$ are four points on a circle. $A C$ and $B D$ intersect at a point $E$ such that $∠ B E C = 130^{o}$ and $∠ E C D = 20^{o}$ . Find $∠ B A C$

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Solution

$A C$ and $B D$ intersect at point $E$ such that

$∠ B E C = 130^{o}$ and $∠ E C D = 20^{o}$

In the given figure, $∠ A C D = ∠ A B D = 20^{o}$ (Angles on the same segment)

Now, $∠ B E C = ∠ A B D + ∠ B A C$ (External angle is the sum of internal opposite angle)

$\Rightarrow ∠ B A C = 110^{o}$

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

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In figure, $A, B, C$ and $D$ are four points on a circle. $A C$ and $B D$ intersect at a point $E$ such that $∠ B E C = 130^{o}$ and $∠ E C D = 20^{o}$ . Find $∠ B A C$