Pupils from Stradbroke Primary School sent in some well-thought out solutions to this problem. Roni explains how they worked out how much further (from 20^°) the point would have to turn to finish the same height above or below the horizontal axis:

1. A whole circle is 360^°, half a circle is 180^°.180^° take away 20^° and then take away another 20^° gives the answer of 140^°.
2. The first 20^° is above the x line and the third 20^° is under the x line so it's always 180^°.
3. A whole circle is 360^°, you take away 20^° and then another 20^°. 20 add 20 equals 40. 360 take away 40 equals 320^°.

So, Roni has concluded that there are three other points where the dot would be the same distance from the horizontal axis as it is for 20^°. Another way of looking at it would be to say that the dot itself would have to be at 20^°, 160^°, 200^°and 340^°.

George tells us how we can work out how far a point at any position on the circle would have to turn to finish the same height above or below the horizontal axis. He agrees that there will be three other solutions:

1. Double the first degree and take it away from 180^°.
2. Add 180^° to the your starting degree.
3. Double the starting degree and take it away from 360^°.

Well done!