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The measure of an exterior angle of a regular polygon is given below. find the measure of an interior angle. then find the number of sides. 72

Respuesta :

brookelynndavi
Well we know that the exterior angle plus the interior angle is equal to 180.
In this case: 180-72=One interior angle.
180-72=108
Knowing that we can now find the number of sides. 
We know that the exterior angles have to add up to 360 and we know ht measure of one of the angles. We divide these numbers and we  can use this to solve for the number of sides.
360/72=number of sides
360/72=5
You have 5 sides and one interior angle measures 108 degrees.

The measure of the interior angles of the regular polygon are equal, and

proportional to the number of sides of the polygon.

  • The measure of an interior angle is 108°.
  • The number of sides of the polygon is 5.

Reasons:

The given parameter are;

The exterior angle of the polygon = 72°

Let x represent the measure of an interior angle of the polygon

The sum of the exterior angle and the adjacent interior angle = 180°

Therefore, x + 72° = 180°

Which gives;

x = 180° - 72° = 108°

The measure of an interior angle, x = 108°

The formula for finding the interior angle of a polygon is [tex]x = \dfrac{(n - 2) \times 180}{n}[/tex]

Therefore;

Where;

n = The number of sides of the polygon

[tex]108 = \dfrac{(n - 2) \times 180}{n}[/tex]

108·n = 180·n - 360

360 = 180·n - 108·n = 72·n

[tex]n = \dfrac{360}{72} = 5[/tex]

The number of sides of the polygon, n = 5

Learn more here:

https://brainly.com/question/18890665

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