Angles - points, lines and parallel lines

Weekly Problem 35 - 2009
Two equilateral triangles have been drawn on two adjacent sides of a square. What is the angle between the triangles?

Weekly Problem 21 - 2009
What is the angle between the two hands of a clock at 2.30?

Weekly Problem 23 - 2008
A triangle has been drawn inside this circle. Can you find the length of the chord it forms?

Weekly Problem 53 - 2007
The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of x?

Weekly Problem 45 - 2007
What is the obtuse angle between the hands of a clock at 6 minutes past 8 o'clock?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

How much do you have to turn these dials by in order to unlock the safes?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?