Angles in Polygons

If you add together the angles in a triangle you always get 180 degrees.

And if you add together the angles in any quadrilateral you get 360 degrees.

What happens with pentagons, or hexagons, or octagons? What about 10-sided or 12-sided or 20-sided shapes?

Is there a pattern? Is there a formula?

Lots to explore here...

Ages 9-13    Printable materials (pdf) - 4 pages of teachers notes and 10 pupil copymasters.

The investigations were very challenging and it made the children think independently and look for patterns, developing their enquiring minds. I would not have thought of presenting such an investigation and in such an open ended way. (Pattern of total of interior angles in 2D shapes V number of sides). The children really enjoyed the level of difficulty and had obviously never looked at such an investigation before.
Year 5 co-ordinator, Woodnewton School