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1.3.1 Angles at a point

Another useful property to remember is that one complete turn is 360°. This means that when there are several angles making up a complete turn, the sum of those angles must be 360°.

For instance, if the angles turned by a Big Wheel at a fairground as it picks up passengers were α, β, γ and δ as shown in the diagram below, then α + β + γ + δ = 360°.

The sum of angles at a point is 360°.

Example 1

Calculate the angle between adjacent spokes of this wheel.


The eight spokes divide the circle up into eight equal parts. Therefore the angle required is found by dividing 360° by 8 to give 45°.