Question

- (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?​

Answer 1

Answer:

- (a) Is it possible to have a regular polygon with measures of each exterior angle as 22 (b) Can it be an interior angle of a regular polygon? Why?

Results in English

एक 22 ख के रूप में प्रत्येक बाहरी कोण के उपायों के साथ एक नियमित बहुभुज के लिए यह एक नियमित बहुभुज क्यों की एक आंतरिक कोण हो सकता है यह संभव है

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Since, answer is not a whole number, thus, a regular polygon with measure of each interior angle as 22⁰ is not possible. ... This can also be proved by another principle; which states that each exterior angle of a regular polygon is equal to 360 divided by number of sides in the polygon. If 360 is divided by 3, we get 120.

Answer 2

The sum of all exterior angles of all polygons is 360°. Also, in a regular polygon, each exterior angle is of the same measure. Hence, if 360° is a perfect multiple of the given exterior angle, then the given polygon will be possible.

(a) Exterior angle = 22°

360° is not a perfect multiple of 22°. 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°.