is it possible to have a regular polygon with measure of each angle as 58° ? why ?
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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 = 58°
360º is not a perfect multiple of 58º. Hence, such polygon is not possible.
(b) Interior angle = 58°
Exterior angle = 180° − 58° = 122°
Such a polygon is not possible as 360° is a perfect multiple of 122°.
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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 = 58°
360º is not a perfect multiple of 58º. Hence, such polygon is not possible.
(b) Interior angle = 58°
Exterior angle = 180° − 58° = 122°
Such a polygon is not possible as 360° is a perfect multiple of 122°.
Was this answer helpful
lavanyakhurana:
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Answer:
(a) Exterior angle=22°
360°is not a perfect multiply of 22°.
hence, such polygon is not possible.
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