Angles in polygons

problem
Quadrilaterals

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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?
problem
Triangles all around

Age

7 to 11

Challenge level

Can you find all the different triangles on these peg boards, and find their angles?
problem
Triangle pin-down

Age

7 to 11

Challenge level

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
problem
Polygon pictures

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?
problem
Triangles in circles

Age

11 to 14

Challenge level

Can you find triangles on a 9-point circle? Can you work out their angles?
problem
Polygon rings

Age

11 to 14

Challenge level

Join pentagons together edge to edge. Will they form a ring?
problem
Star polygons

Age

11 to 14

Challenge level

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
problem
Bow tie

Age

11 to 14

Challenge level

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.