Question

ਇੱਕ ਸਮਭੁਜੀ ਬਹੁਭੁਜ ਦੇ ਹਰੇਕ ਬਾਹਰੀ ਕੋਣ ਦਾ ਮਾਪ 45° ਹੈ । ਭੁਜਾਵਾਂ ਦੀ ਸੰਖਿਆ ਪਤਾ ਕਰੋ । ​

Answer 1

Given:

The dimension of each outer angle of an equilateral polygon is 45°

To find:

The number of arms

Solution:

$\boxed{\bold{Regular\:Polygon}}$ : A regular polygon is any polygon which has equal angles i.e., equiangular and also has equal sides i.e., equilateral.

Let's assume the no. of arms or sides of the equilateral polygon be "n".

The measure of each exterior angles of the polygon = 45°

We know that → the sum of the exterior angles of a polygon is 360°.

Therefore, we can form an equation as:

$The \:measure\: of\: each\: exterior\: angle = \frac{Sum \:of\:exterior\:angles }{No. \:of\: sides\:of\:the\:polygon}$

substituting the values, we get

$\implies 45\° = \frac{360\° }{n}$

$\implies n = \frac{360\° }{45\°}$

dividing both numerators and denominators by 9 on the RHS, we get

$\implies n = \frac{40\° }{5\°}$

$\implies \bold{n = 8}$

Thus, the number of arms or sides of the equilateral polygon is → 8.

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Also View:

If the exterior angle of a regular polygon is 45 degrees, then what is the no. of sides in the polygon and the no. of diagonals?

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How many sides does a regular polygon have if each of its interior angle is 165°

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Answer 2

Answer:

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