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Question

In the given figure ABCD is a cyclic quadilateral; O is the centre of the circle. If BOD= 160,find the measure of BPD= x .The value of x is


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Solution

Consider the arc BCD of the circle. This arc makes BOD = 160 at the centre of the circle and BAD at a point A on the circumference.
BAD = BOD = 80
Now, ABPD is a cyclic quadrilateral.
BAD + BPD = 180
80 + BPD = 180
BPD = 100
BCD = 100 [BPD and BCD are angles in the same segment BCD = BPD ]


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