Mathematics
A circle with center at point O and ∠AOC = 160°.
Statement (1) : Angle x = 100° and angle y = 80°.
Statement (2) : The angle, which an arc of a circle subtends at the center of the circle is double the angle which it subtends at any point on the remaining part of the circumference.
Both statements are true.
Both statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Circles
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Answer
We know that, the angle, subtended by an arc of a circle is double the angle subtended by it at any point on the remaining part of the circle.
So, statement 2 is true.
⇒ ∠AOC = 2x
⇒ 160° = 2x
⇒ x = = 80°
We know that, sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
⇒ x + y = 180°
⇒ 80° + y = 180°
⇒ y = 180° - 80° = 100°
So, statement 1 is false.
Hence, option 4 is the correct option.
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