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Q.

In the figure, arc ABC  of the circle subtends angle of 130 °   at the centre O. If AB is produced to D, then CBD  will be:


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a

60 °  

b

65 °  

c

70 °  

d

130 °   

answer is B.

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Detailed Solution

It is given that arc ABC  of the circle subtends angle of 130 °   at the centre O.
Question ImageFrom figure,
Reflex AOC+AOC= 360 ° Reflex AOC+ 130 ° = 360 ° Reflex AOC= 230 °   As we know that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circle.
So, Reflex AOC=2×ABC    ABC= 1 2 ×Reflex AOC ABC= 1 2 × 230 ° = 115 °   Now, we know the sum of all angles lying on a straight line is 180°.   CBD+ABC= 180 ° CBD+ 115 ° = 180 ° CBD= 65 °  
The value of CBD= 65 °  .
Hence, the correct option is 2.
 
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