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Mathematics

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

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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