Short Answer TypeThe interior angle of a regular is 108°. Find the number of sides of the polygon. Solution: Let there are ‘n’ sides of the regular polygon.
Two regular polygons are such that the ratio of the measures their interior angles is 4 : 3 and the ratio between their number of sides is 2 : 1. Find the number of sides of each polygon.
Given here are some figures. 
(a) Simple curve (b) Simple closed curve (c) Polygon
(d) Convex polygon (e) Concave polygon
What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that).
|
Figure |
|
|
|
|
|
Side |
3 |
4 |
5 |
6 |
|
Angle sum |
180° |
2 x 180° = (4 - 2) x 180° |
3 x 180° = (5 - 2) x 180° |
4 x 180° = (6 - 2) x 180° |
What can you say about the angle sum of a convex polygon with number of sides?
7
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that).
|
Figure |
|
|
|
|
|
Side |
3 |
4 |
5 |
6 |
|
Angle sum |
180° |
2 x 180° = (4 - 2) x 180° |
3 x 180° = (5 - 2) x 180° |
4 x 180° = (6 - 2) x 180° |
What can you say about the angle sum of a convex polygon with number of sides?
8
When n = 8
Substituting n = 8 in the above formula, we have
Sum of interior angles of a polygon having 8 sides
= (n - 2) x 180° = (8 - 2) x 180°
= 6 x 180°
= 1080°
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that).
|
Figure |
|
|
|
|
|
Side |
3 |
4 |
5 |
6 |
|
Angle sum |
180° |
2 x 180° = (4 - 2) x 180° |
3 x 180° = (5 - 2) x 180° |
4 x 180° = (6 - 2) x 180° |
What can you say about the angle sum of a convex polygon with number of sides?
10
Switch
