Question

How many maximum reflex interior angles can a quadrilateral have?

• A. $2$
• B. $1$
• C. $3$
• D. There cannot be any reflex interior angle in quadrilateral

Answer 1

The correct option is B $1$

We know the sum of all the interior angles of quadrilateral is ${360}^o$ and it has total four vertices and four sides.

We also know that reflex angle is greater than ${180}^o$ in measure.

Now, let us check for one interior reflex angle in a quadrilateral.

Here, there are $4$ vertices and vertex $D$ is reflex angle.
$\angle A+\angle B+\angle C+\angle D={360}^o$

If $\angle D>{180}^o$, we get
$\angle A+\angle B+\angle C<{180}^o$
It is possible for a qudrilateral.
So one reflex angle is possible in quadrilateral.



Now, let us check for $2$ interior reflex angles in any quadrilateral.
Consider a quarliaterla PQRS
$\angle P+\angle Q+\angle R+\angle S={360}^o$

If $\angle P\&\angle Q$ are reflex angles.
that means $\angle P>{180}^o\&\angle Q>{180}^o$
then $\angle P+\angle Q$ must be greater than ${360}^o$ which is not possible for the quadrilateral PQRS.