Mathematics
In the adjoining figure, O is the center of the circle. If angle BOC = 140°, the value of x is :
70°
30°
40°
20°
Circles
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Answer
From figure,
⇒ ∠AOC + ∠BOC = 180° [Linear Pair]
⇒ ∠AOC + 140° = 180°
⇒ ∠AOC = 180° - 140° = 40°.
We know that,
Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circumference of the circle.
∴ ∠AOC = 2∠ADC
⇒ 40° = 2x
⇒ x = = 20°.
Hence, Option 4 is the correct option.
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