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°
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 = = 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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