Question

Determine the possible number of sides of an equiangular polygon having one interior angle as ${90}^o.$

• A. Three
• B. Four
• C. Five
• D. Ten

Answer 1

The correct option is B Four

An equiangular polygon is a polygon that has all the interior angles of same measure.

Given: One interior angle is ${90}^o.$
$\therefore$ All the interior angles are ${90}^o.$

A triangle cannot have all the interior angles as ${90}^o$ because sum of three angles of a triangle is ${180}^o$.

Sum of angles of a quadrilateral is ${360}^o$.
Here, if four equal angles of ${90}^o$ are added then we get ${360}^o$.

A quadrilateral with all the interior angles as ${90}^o$ is either a square or a rectangle.
Here, the adjacent sides are perpendicular to each other.


However, with a higher number of sides, i.e., greater than $4,$ a closed figure is not possible with adjacent sides perpendicular to each other.

$\therefore$ Only possible answer is $4.$