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In the adjoining figure, O is the center of the circle. If angle BOC = 140°, the value of x is :

  1. 70°

  2. 30°

  3. 40°

  4. 20°

In the adjoining figure, O is the center of the circle. If angle BOC = 140°, the value of x is. 1. 70° 2. 30° 3. 40° 4. 20°. Model Paper 2, Concise Mathematics Solutions ICSE Class 10.

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 = 40°2\dfrac{40°}{2} = 20°.

Hence, Option 4 is the correct option.

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