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Angles in polygons - Maths - Learning with BBC Bitesize - BBC Bitesize
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Video: What is a polygon?
Working out the sum of internal angles
Pentagon
Hexagon
Heptagon
Octagon
Irregular polygons
Activities
Quiz 1
Quiz 2
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.
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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°
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’s why you then multiply by 180° - that’s 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.
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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°
540° = 3 x 180°
What would one angle be worth in a regular pentagon?
Just divide 540 by the number of angles there are:
540° ÷ 5 = 108°
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Hexagon
Since a hexagon has 6 sides, let’s substitute that amount into the formula:
sum of internal angles = (6 - 2) x 180
720° = 4 x 180
What would one angle be in a regular hexagon?
720° ÷ 6 = 120°
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Heptagon
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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° = 5 x 180°
What would one angle in a regular heptagon be?
900° ÷ 7 = 128. 57° (rounded to 2 decimal places)
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Octagon
Octagons have 8 sides so again, we need to adjust the formula accordingly:
sum of internal angles = (8 - 2) x 180°
1080° = 6 x 180°
In a regular octagon, one angle would be worth:
1080° ÷ 8 = 135°
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Irregular polygons
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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’t be since they are different sizes!
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Activities
Quiz 1
Put your knowledge of interior angles of polygons to the test in this quick quiz.
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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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