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 $158°$