Question
Write True or False and justify your answer in the following: $ABCD$ is a cyclic quadrilateral such that $\angle\text{A}=90^\circ,\angle\text{B}=70^\circ,\angle\text{C}=95^\circ$ and $\angle\text{D}=105^\circ.$
✓
Answer
In a cyclic quadrilateral, the sum of opposite angles is $180^\circ .$
Now, $\angle\text{A}+\angle\text{C}=90^\circ+95^\circ=185^\circ\neq180^\circ$ and $\angle\text{B}+\angle\text{D}=70^\circ+105^\circ=175^\circ\neq180^\circ$
Here, we see that, the sum of opposite angles is not equal to $180^\circ .$
So, it is not a cyclic quadrilateral.
Now, $\angle\text{A}+\angle\text{C}=90^\circ+95^\circ=185^\circ\neq180^\circ$ and $\angle\text{B}+\angle\text{D}=70^\circ+105^\circ=175^\circ\neq180^\circ$
Here, we see that, the sum of opposite angles is not equal to $180^\circ .$
So, it is not a cyclic quadrilateral.
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