Question

Can all the angles of a quadrilateral be right angles?

• A. Yes
• B. No
• C. Maybe
• D. Cannot be determined

Answer 1

The correct option is A Yes

Let us take a quadrilateral $ABCD$ with $AC$ as its diagonal.

In $\Delta ADC$ we have,

$\angle ACD+\angle CDA+\angle DAC={180}^O$ ........$\left(i\right)$ [sum of the angles of a $\Delta ={180}^O]$

Also, in $\Delta ABC$ we have

$\angle ACB+\angle CBA+\angle BAC={180}^O$ ........$\left(ii\right)$ [sum of the angles of a \Delta ={ 180 }^{ O }]$ .

Adding $\left(i\right)$ & $\left(ii\right)$, we have,

$\angle ACD+\angle CDA+\angle DAC+\angle ACB+\angle CBA+\angle BAC={360}^O$

$⟹\angle A+\angle B+\angle C+\angle D={360}^O$

So, the sum of the angles of a quadrilateral is ${360}^O$ .......$\left(iii\right)$.

Now, if each angle is ${90}^o$, then $\angle A+\angle B+\angle C+\angle D={90}^O\times 4={360}^O$ .

It complies with $\left(iii\right)$.

Hence, all the angles of a quadrilateral can be right angles.

That is, the statement is true.

Therefore, option $A$ is correct.