The regular polygon whose exterior angle is-40- is a-Decagon-Octagon-Heptagon-Nonagon-

The correct option is D Nonagon Sum of external angles of any polygon is 360^∘ Since it is a regular polygon, all the exterior angles are equal i.e., 40^∘ each ...

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Standard VIII

Mathematics

Deducing a Formula for Sum of Interior Angles of a Polygon

The regular p...

Question

The regular polygon whose exterior angle is $40^{\circ}$ is a:

Nonagon

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Decagon

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Octagon

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Heptagon

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Solution

The correct option is A
Nonagon

Sum of external angles of any polygon is $360^{\circ}$
Since it is a regular polygon, all the exterior angles are equal i.e., $40^{\circ}$ each.
Exterior angle = $\frac{360 °}{n}$ ; where n is the number of sides.
$\Rightarrow$ n = $\frac{360 °}{40 °}$
$\Rightarrow$ n = 9
It is a nonagon.

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The regular polygon whose exterior angle is 40∘ is a:

The correct option is A Nonagon Sum of external angles of any polygon is 360∘ Since it is a regular polygon, all the exterior angles are equal i.e., 40∘ each. Exterior angle = 360°n; where n is the number of sides. ⇒ n =360°40° ⇒ n = 9 It is a nonagon.

The regular polygon whose exterior angle is $40^{\circ}$ is a: