Angles at a point
Theory
Angles that meet at a point and fill the space all the way round it add up to 360°. To find a missing angle, add the known angles and subtract from \(360^\circ\).
Going once all the way round a point is one full turn, and a full turn is \(360^\circ\).
When several angles meet at a point with no gaps and no overlaps, their sizes add to \(360^\circ\).
To find a missing angle, add the known angles and subtract from \(360^\circ\). A right-angle mark counts as \(90^\circ\).
Three angles at a point, two known.
| Step | Working |
|---|---|
| Fact | angles at a point \(= 360^\circ\) |
| Add known | \(120^\circ + 95^\circ = 215^\circ\) |
| Subtract | \(360^\circ - 215^\circ = 145^\circ\) |
How to find an angle at a point
- Add the angles that are known (count a square mark as \(90^\circ\)).
- Subtract that total from \(360^\circ\).
- Check that all the angles at the point now add to \(360^\circ\).
\(120^\circ + 95^\circ = 215^\circ\), then \(360^\circ - 215^\circ = 145^\circ\).
The third angle is \(145^\circ\).
\(90^\circ + 110^\circ = 200^\circ\), then \(360^\circ - 200^\circ = 160^\circ\).
The third angle is \(160^\circ\).
\(100^\circ + 150^\circ = 250^\circ\), then \(360^\circ - 250^\circ = 110^\circ\).
The third slice is \(110^\circ\).
\(140^\circ + 130^\circ + 90^\circ = 360^\circ\).
They total \(360^\circ\), so yes.
Common pitfalls
Frequently asked questions
What do angles at a point add up to?
They add up to \(360^\circ\), because they make one full turn.
How do you find a missing angle at a point?
Add the angles you know, then subtract from \(360^\circ\). For example \(360^\circ - 215^\circ = 145^\circ\).
Does a right-angle mark count?
Yes. A square mark stands for \(90^\circ\), so add it in with the other angles even though no number is written.
How is this different from angles on a straight line?
Angles at a point fill a full turn and add to \(360^\circ\); angles on a straight line fill a half turn and add to \(180^\circ\).