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What conclusion should be made from the two statements and a question given below?

Is ABCD a cyclic quadrilateral?

I. Points A, B, C and D lie on a circle.

II. ∠B + ∠D = 180°.

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The given question can be answered by any one of the statements but not the other.

The given question can be answered by using either statement alone.

The given question can be answered by using both the statements together but cannot be answered by using either statement.

The given question cannot be answered by using both the statements together. Question Image

answer is C.

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Detailed Solution

We know that a cyclic quadrilateral is circumscribed in a circle and all of its four vertices lie in the circumference of the circle.
Question Image

Also, in cyclic quadrilateral the sum of opposite angle is

1800

. The given statement II is

∠ B + ∠ D = 1800

which is possible only when the points A, B, C and D lie on a circle.
Hence, from the above analysis we can conclude that ABCD is a cyclic quadrilateral.
Therefore, option 3 is correct.

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