Angles - points, lines and parallel lines

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?
problem
Right angles

Age

11 to 14

Challenge level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
problem
Subtended angles

Age

11 to 14

Challenge level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
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
Angular reflection

Age

11 to 14

Challenge level

Weekly Problem 28 - 2013
Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?
problem
Sweeping hands

Age

7 to 11

Challenge level

Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.
problem
Right angle challenge

Age

5 to 7

Challenge level

How many right angles can you make using two sticks?