Angles in polygons

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

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Are these statements always true, sometimes true or never true?

How would you move the bands on the pegboard to alter these shapes?

This problem shows that the external angles of an irregular hexagon add to a circle.

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Can you find all the different triangles on these peg boards, and find their angles?

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?