Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
Drawing the right diagram can help you to prove a result about the angles in a line of squares.
A collection of short problems on Angles, Polygons and Geometrical Proof.