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

Solution:

Given, one exterior angle is 90 degrees.

exterior angle of a polygon is 90 degrees

Each exterior angle will be 180 - 90 = 90 degrees.

We know the sum of exterior angles is 360 degrees.

So, number of sides = 360/90 = 4

the polygon is a square if its exterior angle is 90 degrees

Therefore, the regular polygon has 4 sides.

Summary:

A regular polygon will have 4 sides if each exterior angle measures 90 degrees.

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