Geometry
Angles Around a Point – A Full 360° Turn
Whenever several angles meet at a single point and together make a complete rotation, their measures always sum to 360° – a full turn. This is the natural extension of “angles on a straight line” (180°, a half turn): instead of splitting a straight line, you're splitting an entire rotation around one central point into several angles.
You'll see this rule constantly in diagrams involving spokes, fans, or several lines radiating out from the same central vertex – wherever the angles fully surround a point with no gaps or overlaps, they must add up to 360°.
The Full-Turn Rule
Angles that meet at a single point and fully surround it always sum to 360°. If all but one angle is known, the missing angle is 360° minus the sum of the others.
90 + 80 + 100 + x = 360. 270 + x = 360. x = 90°.
Real-Life Application
- Bicycle wheel spokes: the angles between spokes around the hub sum to 360°.
- Pie charts: the slices of a pie chart are angles around a central point that sum to 360°.
- Roundabouts: the road segments meeting at a roundabout's centre sum to a full 360° turn.
Key Takeaways
- Angles meeting fully around a single point always sum to 360°.
- This extends the straight-line rule (180°) to a complete rotation.
- A missing angle can be found by subtracting the known angles from 360°.