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In the adjoining figure, O is the center of the circle and ∠AOC = 150°, then the value of 2y - x is:

(i) 60°

(ii) 135°

(iii) 45°

(iv) 285°

In the adjoining figure, O is the center of the circle and ∠AOC = 150°, then the value of 2y - x is: (i) 60° (ii) 135° (iii) 45° (iv) 285°. Model Paper 1, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

We know that,

Angle subtended by an arc on the centre of the circle is twice the angle subtended on any other point on the circumference.

∴ 2x = 150°

⇒ x = 150°2\dfrac{150°}{2} = 75°.

We know that,

Sum of opposite angles of a cyclic quadrilateral is 180°.

∴ x + y = 180°

⇒ 75° + y = 180°

⇒ y = 180° - 75° = 105°.

⇒ 2y - x = 2 × 105° - 75° = 210° - 75° = 135°.

Hence, Option 2 is the correct option.

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