Angles - points, lines and parallel lines

problem
Flight path

Age

16 to 18

Challenge level

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
problem
Overlapping squares

Age

7 to 11

Challenge level

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.
problem
Spirostars

Age

16 to 18

Challenge level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
problem
Robo-turn

Age

11 to 14

Challenge level

Weekly Problem 16 - 2007
Can you figure out how far the robot has travelled by the time it is first facing due East?
problem
Semi-regular tessellations

Age

11 to 16

Challenge level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
problem
Tessellating hexagons

Age

11 to 14

Challenge level

Which hexagons tessellate?
problem
Orbiting billiard balls

Age

14 to 16

Challenge level

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
problem
Three tears

Age

14 to 16

Challenge level

Construct this design using only compasses
problem
Dotty relationship

Age

7 to 11

Challenge level

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.
problem
Pegboard quads

Age

14 to 16

Challenge level

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?