Watch: What is a polygon?
Polygons are 2D shapes that have straight sides. Regular polygons have sides and angles that are all the same size.
Let's recap what a polygon is with this quick video.
Working out the sum of internal angles
How would you work out the sum of internal angles in a polygon that has more than 4 sides?
There is a formula that you can use to work out the sum of internal angles that works for all polygons:
Sum of internal angles= (number of sides - 2) x 180掳
Did you know that once you have subtracted 2 from the number of sides, this actually represents the amount of triangles that the polygon is able to be partitioned into from the same vertex?
That鈥檚 why you then multiply by 180掳 - that鈥檚 the sum of the internal angles within a triangle.
Here's how you would change the formula for the different polygons below.
You can even try drawing the shapes out yourself and practise partitioning them into the correct amount of triangles.
Pentagon
Any pentagon has 5 sides. Use the formula to work out what the internal angles total:
sum of internal angles = (5 - 2) x 180掳
540掳 = 3 x 180掳
What would one angle be worth in a regular pentagon?
Just divide 540 by the number of angles there are:
540掳 梅 5 = 108掳
Hexagon
Since a hexagon has 6 sides, let鈥檚 substitute that amount into the formula:
sum of internal angles = (6 - 2) x 180
720掳 = 4 x 180
What would one angle be in a regular hexagon?
720掳 梅 6 = 120掳
Heptagon
All heptagons have 7 sides, so the formula to work out the internal angles would be:
sum of internal angles = (7 - 2) x 180
900掳 = 5 x 180掳
What would one angle in a regular heptagon be?
900掳 梅 7 = 128. 57掳 (rounded to 2 decimal places)
Octagon
Octagons have 8 sides so again, we need to adjust the formula accordingly:
sum of internal angles = (8 - 2) x 180掳
1080掳 = 6 x 180掳
In a regular octagon, one angle would be worth:
1080掳 梅 8 = 135掳
Irregular polygons
In irregular polygons, like this one above, the sum of the interior angles would always be the same, but the value of an individual angles wouldn鈥檛 be since they are different sizes!
Activities
Quiz 1
Put your knowledge of interior angles of polygons to the test in this quick quiz.
Quiz 2
Now have a go at this quiz and try to find the missing angles in the quadrilaterals and regular polygons.
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