A regular polygon has 20 sides work out the sum of the interior angles of the polygon

work out the size of the interior angles

Step-by-step explanation:

The sum of the interior angles of a regular n-gon is given by the formula (n-2)180. Hence, in our case n=20 and we have the answer of 18(180)=3240 degrees.

Step-by-step explanation:

Course menu

Socratic Q&A logo

Search icon

What is the measure of an interior angle of a regular polygon with 20 sides?

Geometry Angles with Triangles and Polygons

1 Answer

mason m

Jan 2, 2016

162

˚

Explanation:

The sum of the interior angles in a regular polygon with

n

sides is found through the formula

180

˚

(

n

−

2

)

Here,

n

=

20

, so the sum of the interior angles is

180

˚

(

20

−

2

)

=

180

˚

(

18

)

=

3240

˚

To find just one angle, divide

3240

˚

by

20

since all

20

angles are congruent.

3240

˚

20

=

162

˚