Question

How many sides does a regular polygon have if the measure of an exterior angle is 24 degree

Answer 1

The regular polygon has 15 sides.

Given : The measure of an exterior angle of a regular polygon is 24 degree.

To find : The number of sides of that regular polygon.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the given regular polygon)

Let, the number of sides of the regular polygon = n

Now, each of the interior angle of the regular polygon will be :

$= \frac{ n - 2}{n} \times 180°$

Now, we know that :

An interior angle of a regular polygon + An exterior angle of a regular polygon = 180°

So,

An interior angle of a regular polygon = 180° - An exterior angle of a regular polygon

In the case of the given regular polygon :

An exterior angle = 24°

So,

An interior angle = (180° - 24°) = 156°

Now, comparing the two measurements of an interior angle of the given regular polygon, we get :

$\frac{n - 2}{n} \times 180 = 156$

$\frac{180n - 360}{n} = 156$

$180n - 360 = 156n$

$180n - 156n = 360$

$24n = 360$

$n = \frac{360}{24}$

$n = 15$

So, number of sides of the regular polygon = n = 15

Hence, the regular polygon has 15 sides.

Answer 2

Answer:

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