Polygonal Angles 1 – Angle Sum
Geometry
Level
1
| Regular -gon | Internal Angle Sum |
| 3 | 180 |
| 4 | 360 |
| 5 | 540 |
| 6 | 720 |
Given the pattern seen in this table, which of the following accurately represents the internal angle sum in terms of ?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
6 solutions
Discussions for this problem are now closed
Let P be a random point in the n-polygon. Then the point(say R) adjacent to adjacent point( say Q) of P if joined to P will form a triangle. Then take the adjacent point of R ( say S) join it to P. Continue this till possible. You will find that you have divided the n-polygon in (n-2) triangles and all the angles of these triangles together form the internal angle of the polygon. So 1 8 0 ∗ ( n − 2 ) gives the total angle of the n-polygon.