Question

1. Is it possible to have a regular polygon with measure of each exterior angle as \(22\degree\)? 
2. Can it be an interior angle of a regular polygon? Why?

Answer 1

The sum of all exterior angles of all polygons is \(360\degree\). 
Also, in a regular polygon, each exterior
angle is of the same measure. 
Hence, if \(360\degree\) is a perfect multiple of the given exterior angle, then the given polygon will be possible.
(a) Exterior angle = \(22\degree\)
\(360\degree\) is not a perfect multiple of \(22\degree\). 

Hence, such polygon is not possible.

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(b) Interior angle = \(22\degree\)
Exterior angle = \(180° - 22° = 158°\)
Such a polygon is not possible as 360° is not a perfect multiple of \(158°\)