"Question 5 (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?
Understanding Quadrilaterals Page 44"
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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°.
(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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