A polygon has three sides.
find the number of sides in a regular polygon when the measure of each exterior angle is 45°
The polygon with exterior angle of 45° is an octagon. An Octagon has 8 sides.
Before solving this problem, we need to be familiar with some concepts:The sum of exterior angles for any regular polygon is ALWAYS equal to 360°The number of interior angles as well as exterior angles is numerically the same as the number of sides of a given polygon. (e.g. Square has 4sides, so it has 4 interior angles and 4 exterior angles; etc.)
Knowing the above mentioned concepts, the problem stated will now have a trivial solution.Solution:
Given that the sum of exterior angles is always equal to 360° and a given regular polygon have an exterior angle of 45° measure, we can now know how many sides that given polygon have.
no. of sides = = = 8 sides .
In reviewing our Plane Geometry, a polygon with 8 sides is called an Octagon.
The polygon has eight (8) sides since the measure of each exterior angle is 45degrees.