Angles - points, lines and parallel lines

problem
Two exterior triangles

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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

Age

5 to 7

Challenge level

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

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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

Age

7 to 11

Challenge level

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

Age

11 to 14

Challenge level

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?