Question

Find the number of sides of a regular polygon, if the exterior angle is one – third of
its interior angle.

Answer 1

Answer:

8 sides

Step-by-step explanation:

A regular polygon is a polygon whose sides are of equal length.

Let us suppose that the interior angle of the regular polygon is given by x

.

Then the exterior angle of the polygon being one-third of the interior angle of the same regular polygon is given by 13x

.

Now we know the exterior angle property for a regular polygon which says that the sum of the adjacent interior and exterior angle is 180∘

.

Using this we get that

13x+x=180∘

On solving the above equation to find the value of x

, we get

x(13+1)=180∘

⇒x(43)=180∘

⇒x=34×180∘

⇒x=3×45∘

⇒x=135∘

Thus, the interior angle of the regular polygon is given by 135∘

.

Thus, the exterior angle of the regular polygon is given by 135∘3=45∘

.

Now the number of sides of the regular polygon is given by 360exteriorangle

.

Substituting the value of the exterior angle of the given polygon in the above formula we get,

36045=8

Therefore the given regular polynomial has 8 sides. Hence it is a regular octagon.

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