$□ A B C D$ is a cyclic quadrilateral. $m (a r c A B C) = 220^{0}$ .

The $∠ A B C$ in degree is

130

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110

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Solution

The correct option is B 70
$G i v e n - A B C D i s a c y c l i c q u a d r i l a t e r a l i n t h e c i r c l e w i t h c e n t r e O . m (a r c A B C) = 220^{o} . T o f i n d o u t - ∠ A B C = ? S o l u t i o n - W e j o i n A C . m (a r c A B C) = 220^{o} m e a n s m ∠ A O C (r e f l e x) = 220^{o} . ∴ ∠ A O C = 360^{o} - 220^{o} = 140^{o} . N o w ∠ A O C h a s b e e e n s u b t e n d e d b y t h e c h o r d A C t o O a n d ∠ A B C h a s b e e e n s u b t e n d e d b y t h e c h o r d A C t o t h e c i r c u m f e r e n c e o f t h e s a m e c i r c l e a t B . ∴ ∠ A B C = \frac{1}{2} \times ∠ A O C = \frac{1}{2} \times 140^{o} = 70^{o} . A n s - O p t i o n B .$

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Similar questions

ABCD is a cyclic quadrilateral, in which $∠ D B C = 80^{\circ}$ and $∠ B A C = 40^{\circ}$ . $∠ B C D$ (in degrees ) = ___ .

If ABCD is a cyclic quadrilateral. What will be the value of $x$ (in degrees)?

A B C D

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∠ A B C = 60^{\circ}

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