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Question

In the given figure, P and Q are the centres of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x.


  1. 140

  2. 150

  3. 130

  4. 120


Solution

The correct option is C

130


In the given figure, 
APB=2ACB        [Angle subtended by an arc at the center is double the angle subtended by it at any other point on the remaining part of the circle]
ACB=65

Now, ACB+BCD=180       [Linear pair angles]
BCD=115
ReflexBQD=2BCD=2×115=230
Also, x + ReflexBQD=360
x+230=360
x=360230=130
 

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