Question

5.) (a) Is it possible to have a regular polygon with measure of each exterior angle as (b) Can it be an interior angle of a regular polygon? Why?​

Answer 1

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HINT : Here, the property of a regular polygon is used (i.e., the sum of all the exterior angles which are equal to each other of a regular polygon is always 360° .

A) No, it is not possible to have a regular polygon with measure of each exterior angle of 22° because 22° is not a multiple of 360°. Since, the sum of all the exterior angles of a regular polygon is always 360° and all the exterior angles of a regular polygon are equal in measure .

B) If the interior angle of a regular polygon is 22° , then the measure of exterior angle of that regular polygon will be (180° − 22°) = 158° . Clearly , 158° is not a multiple of 36003600. So, it is not possible to have a regular polygon with a measure of each interior angle of 22° .

NOTE - In these types of problems, if the interior angle of the regular polygon is given then it is converted into the exterior angle of the regular polygon. Then using properties of a regular polygon like the sum of all the exterior angles is always equal to 360° and each exterior angle is equal, we have to check whether these properties hold true or false. If they hold then that regular polygon is possible else, it is not.