Angles - points, lines and parallel lines

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

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

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

Symmetric Angles

Age

14 to 16

Challenge level

This diagram has symmetry of order four. Can you use different geometric properties to find a particular length?
problem

On Time

Age

11 to 14

Challenge level

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?
problem

Similarly So

Age

14 to 16

Challenge level

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
problem

Flower

Age

16 to 18

Challenge level

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.
problem

Tessellating Hexagons

Age

11 to 14

Challenge level

Which hexagons tessellate?
problem

Right Angle Challenge

Age

5 to 7

Challenge level

How many right angles can you make using two sticks?
problem

Take the Right Angle

Age

7 to 11

Challenge level

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.