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Angles in Alternate Segments

In the figure...

Question

In the figure, ABC is a circle with centre O and reflex $∠$ AOB $= 250^{o}$ . Find $x$ .

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Solution

Given, reflex $∠ A O B = 250^{o}$
$∠ A O B = 360 - r e f l e x ∠ A O B ∠ A O B = 360 - 250 ∠ A O B = 110$
$A C B O$ is a cyclic quadrilateral
$∠ A C B + ∠ A O B = 180 ∠ A C B = x = 180 - ∠ A O B x = 180 - 110 x = 70^{o}$

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