Angles in polygons

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Weekly Problem 50 - 2012
The diagram shows a regular dodecagon. What is the size of the marked angle?

Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?

Weekly Problem 53 - 2012
ABCDEFGHI is a regular nine-sided polygon (called a 'nonagon' or 'enneagon'). What is the size of the angle FAE ?

Weekly Problem 15 - 2012
How many of the five properties can a heptagon have?

How can the school caretaker be sure that the tree would miss the school buildings if it fell?

Weekly Problem 9 - 2012
What is the angle QPT in this diagram?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.