Mathematics
In the given figure, O is the centre of the circle, ∠AOB = 40° and ∠BDC = 100°. The measure of ∠OBC is :
40°
80°
60°
20°
Circles
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Answer
We know that,
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
∴ ∠ACB = ∠AOB
∠ACB = = 20°
In ΔBDC, the sum of all angles is 180°
∠OBC + ∠BDC + ∠ACB = 180°
∠OBC + 100° + 20° = 180°
∠OBC = 180° - 120°
∠OBC = 60°
Hence, option 3 is the correct option.
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Related Questions
In the given figure, if O is the centre of the circle, then the value of x is :
40°
50°
70°
30°
In the given figure, O is centre of the circle.
If ∠AOC = 130°, then the value of x is :25°
50°
65°
40°
ABCD is a cyclic quadrilateral. If ∠BAD = (2x + 5)° and ∠BCD = (x + 10)°, then x is equal to :
65°
45°
55°
5°
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
A is false, R is true
Both A and R are true
Both A and R are false
