Question

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

The statement is:

• A. true.
• B. false.
• C. true in special condition.
• D. Data insufficeint

Answer 1

The correct option is B false.

Given, $ABCD$ is a cyclic quadrilateral where $\angle A={90}^o,\angle B={70}^o,\angle C={95}^o$ & $\angle D={105}^o.$

Since $ABCD$ is a cyclic quadrilateral,

then $\angle A+\angle C={180}^o$ and $\angle B+\angle D={180}^o$......$\left(i\right)$(The sum of the opposite angles of a cyclic quadrilateral is ${180}^o)$

But here, $\angle A+\angle C={90}^o+{95}^o={185}^o$ and $\angle B+\angle D={70}^o+105^o={175}^o.$

This is a contradiction to $\left(i\right)$.

That is, the statement is false.

Hence, option $B$ is correct.