a decadogon
Icosihenagon
Each interior angle measures 162.'857142' degrees recurring '857142'
The number of triangles formed by the diagonals of a 21 sided polygon is C(21,3) = 21x20x19/3x2x1 = 1,330.
Let the measure of the first angle be x⁰. So that the second angle would be (x + 21)⁰, and the third one would be (x - 15)⁰.Since the sum of angle measures in a triangle is 180⁰ we have:x + x + 21 + x - 15 = 1803x = 174x = 58Thus, the first angle is 58⁰, the second angle is 79⁰, and the third angle is 43⁰.
So, the Sum of the interior angles for a 21 – sided polygon is equal to 3420°.
21
The sum of the interior angles of a polygon is 2n - 4 right angles where n is the number of sides. When n = 21 then 2n - 4 = 42 - 4 = 38 right angles = 38 x 90 = 3420°. NOTE : If the polygon is a regular polygon then each interior angle measures 3420 ÷ 21 = 162.86°.
a decadogon
Icosihenagon
Icosihenagon
Dodectagon
Each exterior angle is 360/21 = 17.1429 deg so each interior angle is 180 - exterior angle = 162.8571 degrees.
Each interior angle measures 162.'857142' degrees recurring '857142'
180*(21-2) = 180*19 = 3420 degrees.
38 x 90 ie 3420o
The sum of the interior angles of a polygon with n sides is 180(n-2). Here is my explanation about it.http://math4allages.wordpress.com/2009/10/21/angle-sum/