You might like to have a look at Nine-Pin Triangles
before trying this problem.
How many different triangles can you draw on a circular pegboard which has four equally spaced pegs?
What are the angles of each triangle?
If you have a six-peg circular pegboard, how many different triangles are possible now?
What are their angles?
How many different triangles could you draw on an eight-peg board?
Can you find the angles of each?
You may like to use the interactivity to try out your ideas. When you have selected the number of dots you need, select the line drawing tool, then click on two dots to draw a line between them.
Many thanks to Geoff Faux who introduced us to the merits of the nine-pin circular geoboard.
For further ideas about using geoboards in the classroom, please see Geoff's publications available through the Association of Teachers of Mathematics (search for 'geoboards').