Angles in polygons

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Weekly Problem 30 - 2011
Three touching circles have an interesting area between them...

Weekly Problem 1 - 2011
Use facts about the angle bisectors of this triangle to work out another internal angle.

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

Weekly Problem 44 - 2010
Extend two of the sides of a nonagon to form an angle. How large is this acute angle?

Weekly Problem 39 - 2010
If you know three lengths and an angle in this diagram, can you find another angle by calculation?

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Why does this fold create an angle of sixty degrees?

Weekly Problem 50 - 2008
The lengths SP, SQ and SR are equal and the angle SRQ is x degrees. What is the size of angle PQR?