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$A B C D$ is a cyclic quadrilateral such that $A = 90 °, B = 70 °, C = 95 °$ and $D = 105 °$ . The statement is:

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True

False

answer is B.

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Detailed Solution

Given,

A B C D

is a cyclic quadrilateral where,

∠ A = 90 °, ∠ B = 70 °, ∠ C = 95 °

and

∠ D = 105 °

Since

A B C D

is a cyclic quadrilateral, then
⇒

∠ A + ∠ C = 180 °

⇒

∠ B + ∠ D = 180 °

…. (1)
Since, the sum of the opposite angles of a cyclic quadrilateral is

180 °

.
But here,

∠ A + ∠ C = 90 ° + 95 ° = 185 °

and

∠ B + ∠ D = 70 ° + 105 ° = 175 °

Therefore, the given statement is false.
The correct statement is that the quadrilateral ABCD is not cyclic as its sum of opposite angles is not equal to 180°.
Hence, the correct option is 2.

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