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Question
(a) Is it possible to have a regular polygon with measure of eachexterior angle as 22°?
(b) Canit be an interior angle of a regular polygon? Why?
(a) Is it possible to have a regular polygon with measure of eachexterior angle as 22°?
(b) Canit be an interior angle of a regular polygon? Why?
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Solution
The sum ofall exterior angles of all polygons is 360º. Also, in a regularpolygon, each exterior angle is of the same measure. Hence, if 360ºis a perfect multiple of the given exterior angle, then the givenpolygon will be possible.
(a) Exteriorangle = 22°
360º is not a perfect multiple of 22º. Hence, such polygonis not possible.
(b) Interiorangle = 22°
Exterior angle = 180° − 22° = 158°
Such a polygon is not possible as 360° is not a perfect multipleof 158°.
The sum ofall exterior angles of all polygons is 360º. Also, in a regularpolygon, each exterior angle is of the same measure. Hence, if 360ºis a perfect multiple of the given exterior angle, then the givenpolygon will be possible.
(a) Exteriorangle = 22°
360º is not a perfect multiple of 22º. Hence, such polygonis not possible.
(b) Interiorangle = 22°
Exterior angle = 180° − 22° = 158°
Such a polygon is not possible as 360° is not a perfect multipleof 158°.
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