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Angle sum in a polygon


If we know that the angles in a triangle add up to 180°, we can use this fact to work out the total angle sum inside any polygon. This is sometimes called the interior angle sum (interior is just another word for inside - think interior designer!). 

If we pick a corner on a polygon and join that corner to each other corner, we form triangles inside. Each triangle has an angle sum of 180°.

For example, in a pentagon, we form three triangles. Each has an angle sum of 180°, so the total angle sum inside a pentagon must be 180° x 3 = 540°.

The angle sums of polygons are as follows:
Triangle = 180°
Quadrilateral = 360°
Pentagon = 540°
Hexagon = 720°
Heptagon = 900°
Octagon = 1080°

The number of triangles is always two less than the number of sides. We can use this to write a general formula linking the number of sides to the interior angle sum: Interior angle sum = (n - 2) x 180.
Angles in polygons | NorledgeMaths
Click to watch the video tutorial (via YouTube)

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First Steps

What is a polygon?
Naming polygons
Angles in a triangle
Angles in a quadrilateral
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Next Steps

Next Steps

Interior angles in regular polygons
Exterior angles

External links

  • BBC Bitesize: Notes on angle sums of polygons, with a couple of problems to try.
  • Mymaths: Lesson on angle sums of polygons. Test yourself with the online homework.
  • IXL: Test yourself with this online worksheet. It has full solutions for incorrect answers so you can find out where you have gone wrong.
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