Mathematics
ABCD is a cyclic quadrilateral. If ∠BAD = (2x + 5)° and ∠BCD = (x + 10)°, then x is equal to :
65°
45°
55°
5°
Circles
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Answer
In a cyclic quadrilateral, opposite angles are supplementary.
Since ∠BAD and ∠BCD are opposite angles,
(2x + 5)° + (x + 10)° = 180°
3x + 15 = 180°
3x = 165°
x = 55°
Hence, option 3 is the correct option.
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In the given figure, O is centre of the circle.
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In the given figure, O is the centre of the circle, ∠AOB = 40° and ∠BDC = 100°. The measure of ∠OBC is :
40°
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Assertion (A): In the given figure, if O is the centre of the circle, then ∠ACB = 40°.
Reason (R): Angle at the centre is double the angle at the remaining part of the circle.
A is true, R is false
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Assertion (A): In the figure, ∠ACB = 70°.
Reason (R): Opposite angles of a cyclic quadrilateral are equal.
A is true, R is false
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