It was through this exercise that I visualised that a pentagon was made up of 3 triangles and the properties of each triangle is 180° therefore making a pentagon 540°. Then I tried dividing the pentagon into a triangle and a trapezium and added up their interior angles (180° + 360° = 540°), and I have 540° too.
I was taught in school to remember the individual polygons angles; I was not brought through on how we can visualise and understand the parts making up of these polygons.
I went on trying out with the rest of the polygons and realised a pattern in the calculation of the interior angles of any polygons, see pattern below:
shapes | sides | Sum of interior angles |
triangle | 3 | 180° |
quadrilateral | 4 | 2 x 180° = 360 |
pentagon | 5 | 3 x 180° = 540° |
hexagon | 6 | 4 x 180° = 720° |
heptagon | 7 | 5 x 180° = 900° |
octagon | 8 | (8 - 2) x 180° = 1080° |
nonagon | 9 | (9 – 2) x 180° = 1260° |
decagon | 10 | (10 – 2) x 180° = 1440° |
Any polygon | n | (n-2) x 180° |
50 sided polygon | 50 | (50 -2) x 180° = 8640° |
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