Answered

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What is the measure of each exterior angle of a regular polygon whose interior angle measures have a sum of 5400 degrees?

Sagot :

Answer:

32 vertices

Step-by-step explanation:

Sum of the interior angles of a polygon = 5400 deg.

(n-2)*180 = 5400, or

n-2 = 30, or

n = 32.

So the polygon has 32 sides.

It has 30 triangles.

32(32–3)/2 = 464 diagonals

32 vertices.

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The measure of each exterior angle of a regular polygon is 11.25°

The measure of an interior angle of a polygon is given by the formula:

sum of angles = (n -2)180°

GIven that the sum of angles is 5400°

Then;

5400° (n - 2)180°

5400°/180° = (n - 2)

30° = n - 2

n = 30+2

n = 32 sides

Similarly, for an exterior angle, the sum of all the exterior angles is equal to 360°.

For a 32 sided polygon, the measure of the exterior angles will be:

= 360°/32

= 11.25°

Learn more about polygons here:

https://brainly.com/question/12871911?referrer=searchResults

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