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

Question

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

KnowledgeBoat · Accepted Answer

(i) 170° According to the properties of a polygon, if there are n sides, then each of its interior angles is . Given that each interior angle is 170°, ⇒ = 170° ⇒ (2n \- 4) x 90° = 170°n ⇒ 180°n \- 360° = 170°n ⇒ 180°n \- 170°n = 360° ⇒ 10°n = 360° ⇒ n = ⇒ n = 36 Hence, a regular polygon is possible when each interior angle is 170°. (ii) 138° According to the properties of a polygon, if there are n sides, then each of its interior angles is . Given that each interior angle is 138°, ⇒ = 138° ⇒ (2n \- 4) x 90° = 138°n ⇒ 180°n \- 360° = 138°n ⇒ 180°n \- 138°n = 360° ⇒ 42°n = 360° ⇒ n = ⇒ n = ⇒ n = Hence, a regular polygon is not possible when each interior angle is 138°.

Mathematics

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

Geometrical Shapes

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Mathematics

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

Geometrical Shapes

Related Questions

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

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

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

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