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The sum of the interior angles of s regular polygon is 3960, how many sides does it have?
What is the measure of each interior angle?
What is the measure of each exterior angle?

Respuesta :

musiclover10045

The equation for the sum of interior angles is :

Sum = (n-2) x 180, where n is the number of sides.

Replace sum with the given sum:

3960 = (n-2) x 180

Divide both sides by 180:

22 = n-2

Add 2 to each side:

24 = n

It has 24 sides.

For Each interior angle, divide the total sum by the number of sides:

3960 / 24 = 165 degrees

The interior and exterior angle needs to equal 180 degrees. To find the exterior angle, subtract the interior angle from 180:

180 - 165 = 15 degrees.

Cetacea

Each interior angle = 165 degree.

Each exterior angle = 15 degree.

Let: there are n sides.

So the sum of the interior angles is 180(n-2).

According to the question:

[tex]180(n-2)=3960\\ n-2=22\\ n=24[/tex]

So each interior angle = 3960/24 = 165 degree.

Each exterior angle = 180 - 165 = 15 degree.

Learn more: https://brainly.com/question/20521181

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