MathematicsState true/ false: ABCD is a cyclic quadrilateral such that A=90o,B=70o,C=95oand D=105o.

State true/ false:

$ABCD$ is a cyclic quadrilateral such that $A = 90^{o}, B = 70^{o}, C = 95^{o}$ and $D = 105^{o} .$

Given,

ABCD

is a cyclic quadrilateral where

∠ A = 90^{o}, ∠ B = 70^{o}, ∠ C = 95^{o}

∠ D = 105^{o} .

Construct a figure with the given data,

We know that,
In a cyclic quadrilateral sum of opposite angles are supplementary.
Then,

∠ A + ∠ C = 180^{o}

and

∠ B + ∠ D = 180^{o}

......

(i)

But here,

∠ A + ∠ C = 90^{o} + 95^{o} = 185^{o}

∠ B + ∠ D = 70^{o} + 10 5^{o} = 175^{o}

This is a contradiction to

(i)

.
Hence, the statement is false.
ABCD is not a cyclic quadrilateral.
Therefore, option 2 is correct.

JEE