Question

Find the number of sides of a regular polygon whose each exterior angle has a measure of 450

Answer 1

Answer:

Step-by-step explanation:

Total measure of ext. angles=360

Measure of each=45

NO. of sides=360/45=8

Therefore,the answer is 8.

Hope it helps

Answer 2

The number of sides of a regular polygon whose each exterior angle has a measure of $45\°$ is 8

Method 1:

Given, that the exterior of a regular polygon is $45\°$

Let the number of sides be n

We know, in a regular polygon, the sum of all the exterior angles is $360\°$

$\therefore n\times 45\°=360\°\\\Rightarrow n=\frac{360\°}{45\°}=8$

Thus, the number of sides in the regular polygon is 8.

Method 2:

Given, that the exterior of a regular polygon is $45\°$

$\therefore$ Each interior angle = $180\°-45\°=135\°$

This is because the interior and exterior angles are supplementary.

We know, The sum of the interior angles in a polygon with 'n' sides is $(2n - 4)90\°$

The sum of interior angles =

$no.\ of\ sides\times each\ interior\ angle=n\times 135\°\\\therefore 135\°n=(2n-4)90\°\\\Rightarrow 135\°n=180\°n-360\°\\\Rightarrow 360\°=45\°n\\\Rightarrow n=\frac{360\°}{45\°}=8$

To learn to solve more questions involving regular polygons, click on the link below:

https://brainly.in/question/1844156

https://brainly.in/question/12377734

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