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On Time

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?

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Right Time

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

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Estimating Angles

How good are you at estimating angles?

Shogi Shapes

Age 11 to 14 Challenge Level:

Here are a couple of methods you could use to work out the interior angles of a regular nine-sided polygon (a nonagon):
 
1.
 nonagon
Imagine taking a walk around a regular nine-sided park.
The second picture shows the angle you need to turn through when you reach the first corner.
The third picture shows all the angles you turn through when you walk once round the park.
What angle do you turn through altogether?
What must each exterior angle (the red angles) be?
What must each interior angle be?
 
 
nonagon split into isosceles triangles


2. Here is a regular nonagon:

It has been divided into nine isosceles triangles.
What is the total of all the angles in all the triangles?

Now subtract the angles at the centre of the nonagon to work out the total of all the interior angles of the nonagon.


 
 
Can you adapt these methods for any regular polygon?