Mathematics
Assertion (A) : In the figure below, O is the center of the circle and ∠AOC = 160°. Then x = 100° and y = 80°.
Reason (R) : The angle, which an arc of a circle subtends at the centre of the circle is double that which it subtends at any point on the remaining part of the circumference.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Circles
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Answer
We know that,
The angle, which an arc of a circle subtends at the centre of the circle is double that which it subtends at any point on the remaining part of the circumference.
From figure,
⇒ 2x = ∠AOC
⇒ 2x = 160°
⇒ x = = 80°.
We know that,
Sum of opposite angles in a cyclic quadrilateral = 180°.
⇒ x + y = 180°
⇒ 80° + y = 180°
⇒ y = 180° - 80° = 100°.
∴ Assertion (A) is false and Reason (R) is true.
Hence, Option 2 is the correct option.
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