Question

is it possible to have a regular polygon each of whose interior angle is 90°​

Answer 1

Answer:

Suppose polygon has n sides,

then the sum of all the interior angles = (n-2)×180° and

here n is no of sides

each interior angle is = ((n−2)∗180°)/n

above formula

this is equal to n×45°.

Hence 180n -360 =45n

➡ 135n =360 or n = (360°/135) =8/3.

As n should be a positive integer, this shows that it is not possible to have such a polygon...