Is it possible to have a regular polygon whose each exterior angle is:
(i) 80°
(ii) 40% of a right angle

Question

Is it possible to have a regular polygon whose each exterior angle is: (i) 80° (ii) 40% of a right angle

KnowledgeBoat · Accepted Answer

(i) 80° According to the properties of a polygon, if there are n sides, then each of its exterior angles is . Given that each exterior angle is 80°, ⇒ = 80° ⇒ n = ⇒ n = 4.5 Hence, a regular polygon is not possible when each exterior angle is 80°. (ii) 40% of a right angle is: = 40% x 90° = = = 36° According to the properties of a polygon, if there are n sides, then each of its exterior angles is . Given that each exterior angle is 36°, ⇒ = 36° ⇒ n = ⇒ n = 10 Hence, a regular polygon is possible when each exterior angle is 40% of a right angle.

Mathematics

Is it possible to have a regular polygon whose each exterior angle is:
(i) 80°
(ii) 40% of a right angle

Geometrical Shapes

Related Questions

Is it possible to have a regular polygon whose each interior angle is:
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(ii) 138°

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Mathematics

Is it possible to have a regular polygon whose each exterior angle is:(i) 80°(ii) 40% of a right angle

Geometrical Shapes

Related Questions

Is it possible to have a regular polygon whose each interior angle is:(i) 170°(ii) 138°

Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.

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Is it possible to have a regular polygon whose each exterior angle is:
(i) 80°
(ii) 40% of a right angle

Is it possible to have a regular polygon whose each interior angle is:
(i) 170°
(ii) 138°