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

Is ΔABC right – angled at B?

I. ABCD is a cyclic quadrilateral.

II. ∠D = 90°

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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

It is given that ABCD is a cyclic quadrilateral.
Question Image

We know that a cyclic quadrilateral is drawn inside a circle with each of its corner touching the circumference of the circle.
Also, ABCD is a cyclic quadrilateral, the opposite angles of which add up to

1800

.
From the figure, the angle opposite to

∠ D

∠ B

.
So,

∠ B + ∠ D = 1800 ⇒ ∠ B + 900 = 1800 ⇒ ∠ B = 900

So, the value of

∠ B = 900

.
Therefore, option 3 is correct.

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