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(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Asked by Santosh Last Modified
Answer The sum of all exterior angles of all polygons is 360º. Also, in a regular polygon, each exterior angle is of the same measure. Hence, if 360º is a perfect multiple of the given exterior angle, then the given polygon will be possible.
(a) Exterior angle = 22°
360º is not a perfect multiple of 22º. Hence, such polygon is not possible.
(b) Interior angle = 22°
Exterior angle = 180° − 22° = 158°
Such a polygon is not possible as 360° is not a perfect multiple of 158°.
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(a) sum of exterior angles of a polygon is 360°. Also in regular polygon all exterior angles have same value.hence 360 should be a multiple of exterior angle .
360/22=16.36, not a perfect multiple
so 22°cannot be an exterior angle of regular polygon.
(b)sum of each pair of interior and exterior angle of a polygon is 180°.
if interior angle=22°
exterior angle=180-22=158°
since it is a regular polygon,
360/158 should be an integer, but it is not, hence not possible.
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