Mathematics
If O is the center of the circle find the value of x in the following figure (using the given information) :
Circles
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Answer
From figure,
ABCD is a cyclic quadrilateral.
By property of cyclic quadrilateral — An exterior angle of cyclic quadrilateral is equal to opposite interior angle.
We get,
∠BAD = ∠DCE = 80°
Arc BD subtends ∠BOD on center and ∠BAD at point A of the circle.
From figure,
∠BOD = 360° - x°
∴ ∠BOD = 2∠BAD (∵ as angle subtended on center of circle is double the angle subtended on any other part.)
⇒ 360° - x° = 2 × 80°
⇒ x° = 360° - 160°
⇒ x° = 200°.
Hence, the value of x = 200.
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