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By drawing all the diagonals from one vertex, the polygon is divided up into triangles. The sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles.

With n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so:

sum_of_interior_angles = 180 x (number_of_sides - 2)

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Q: How can you determine the sum of the interior angles of a given polygon?
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How can you determine the sum of the exterior angles of a given polygon?

You can do it by memorizing this statement:" The sum of the exterior angles of every polygon is 360 degrees. "


What is the sum of interior angles of a icosagon?

That will depend on what type of isogon it is because an isogon is the name given to any regular polygon whose interior angles are equal.But in the general: (n-2)*180 = sum of interior of any polygon whereas 'n' is the number of sides of the polygon.


Sum of angles of a nonagon?

The sum of the interior angles of a nonagon is 1260 degrees. A nonagon is a nine-sided polygon in geometry. The formula to find the sum of interior angles in a polygon is given by the formula [n-2] x 180 degrees, where n represents the number of sides.


Given an interior angle how do you find the sum of exterior angles of a polygon?

Given a shape as such... ______________________________________ / A=72 B=65 \ \ / \_C=105__________________D=110_______/ (sorta) You take the interior angles that you have and subtract them from 360 to get their supplementary angles, which would be the measure of the outside angles corresponding to the interior angles Measure of <A= 72- so 360- 72=288*; so the measure of the exterior angle corresponding to <A is 288* You can do the same thing for the rest of the angles in the polygon. Hope it helps...


What is the sum of the interior angle measures of a 40- sided convex polygon?

The sum of the interior angles of a convex polygon with n sides is given by (n-2)x180o. So for a 40 sided polygon n=40; thus (40-2)x180o = 38x180o = 6840o.

Related questions

What is sum of the interior angles of a polygon with three sides?

the sum of the interior angles of a 3 sided polygon is = 180 degrees. the sum of the interior angles of any polygon is given by 540/n. in this case n is = 3


What polygons interior angles equal 8640 degrees?

A polygon with 50 sides, given the sum of all the interior angles in 8640.


How can you determine the sum of the exterior angles of a given polygon?

You can do it by memorizing this statement:" The sum of the exterior angles of every polygon is 360 degrees. "


What is the sum of interior angles of a icosagon?

That will depend on what type of isogon it is because an isogon is the name given to any regular polygon whose interior angles are equal.But in the general: (n-2)*180 = sum of interior of any polygon whereas 'n' is the number of sides of the polygon.


What is the sum of the interior angles if the exterior angles are 24?

The sum of the interior angles of any polygon is equal to (n-2) * 180 degrees, where n is the number of sides of the polygon. Since the exterior angles of a polygon are supplementary to the interior angles, if the exterior angles are 24 degrees, the interior angles would be 180 - 24 = 156 degrees.


How do you determine the number of angles of a polygon given the number of sides?

The two numbers are the same.


What is the relationship between interior angles and the sum of the exterior angles of a given polygon?

There isn't one. The sum of the exterior angles is always 360 degrees, the sum of the interior angles varies depending on the number of sides.


What is the rule for finding out the sum interior angle of a polygon?

To find the sum of the interior angles and the sum of the exterior angles of any polygon. To review linear measurement to the nearest sixteenth of an inch and angle measurement to the nearest degree. To construct a polygon and its exterior angles given the number of sides. hope this helped


Sum of angles of a nonagon?

The sum of the interior angles of a nonagon is 1260 degrees. A nonagon is a nine-sided polygon in geometry. The formula to find the sum of interior angles in a polygon is given by the formula [n-2] x 180 degrees, where n represents the number of sides.


Given an interior angle how do you find the sum of exterior angles of a polygon?

Given a shape as such... ______________________________________ / A=72 B=65 \ \ / \_C=105__________________D=110_______/ (sorta) You take the interior angles that you have and subtract them from 360 to get their supplementary angles, which would be the measure of the outside angles corresponding to the interior angles Measure of <A= 72- so 360- 72=288*; so the measure of the exterior angle corresponding to <A is 288* You can do the same thing for the rest of the angles in the polygon. Hope it helps...


How do you find the number of sides in an equiangular polygon given the measures of the interior angles?

Type your answer here... The sum of the angles in all polygons is 360 degrees. Thus, if you know the measure of the interior angles you can divide 360 by the measurement to find out how many interior angles and sides there are.


What is the sum of the measures in degrees of the interior angles of an 18 sided figure?

The sum of the interior angles of an n-gon is given by the formula (n-2)(180) where n is the number of sides of the polygon. Thus, the sum of the interior angles of an 18-gon is (18-2)(180) = 2880.