Question

How many sides does a regular polygon have if one exterior angle is 90 degrees? 3 4 5 6?

Answer 1

4 sides

B is correct

Explanation:

A regular polygon has each exterior angle is equal.

The sum of all angle of exterior angles of regular polygon is 360°

For given regular polygon each exterior angle is 90°

Let use n number of side of polygon or n exterior angles.

Total sum of exterior angles = 90n

It must be equal to 360° because sum of all exterior angles.

90n = 360°

n = 4

Hence, The number of sides of regular polygon whose each exterior angle 90° is 4

Answer 2

The easiest way to do this is to find out the interior angle and divide that number into 360. (The figure is regular meaning all sides are equal. And so are all interior angles).

The interior angle is always the supplement of the exterior angle. In this case 180 - 90 = 90 which is the interior angle. The regular figure you have drawn is a square. It has 4 sides.