Angles on a straight line
Theory
Angles that sit side by side on a straight line always add up to 180°. To find a missing angle, subtract the known angles from \(180^\circ\).
A straight line is a half turn, and a half turn is \(180^\circ\).
When two or more angles sit together along a straight line, with no gaps and no overlaps, their sizes add to \(180^\circ\).
To find a missing angle on a straight line, subtract the known angles from \(180^\circ\).
Two angles on a line, one known.
| Step | Working |
|---|---|
| Fact | angles on a line \(= 180^\circ\) |
| Known angle | \(65^\circ\) |
| Subtract | \(180^\circ - 65^\circ = 115^\circ\) |
How to find an angle on a straight line
- Add the angles that are known.
- Subtract that total from \(180^\circ\).
- Check that all the angles on the line now add to \(180^\circ\).
\(180^\circ - 65^\circ = 115^\circ\).
The other angle is \(115^\circ\).
\(180^\circ - 45^\circ = 135^\circ\).
The missing angle is \(135^\circ\).
\(35^\circ + 65^\circ = 100^\circ\), then \(180^\circ - 100^\circ = 80^\circ\).
The third angle is \(80^\circ\).
\(120^\circ + 60^\circ = 180^\circ\).
They total \(180^\circ\), so yes.
Common pitfalls
Frequently asked questions
What do angles on a straight line add up to?
They add up to \(180^\circ\), because a straight line is a half turn.
How do you find a missing angle on a straight line?
Add the angles you know, then subtract from \(180^\circ\). For example \(180^\circ - 65^\circ = 115^\circ\).
Do three angles on a line still add to 180?
Yes. However many angles sit side by side on the line, together they add to \(180^\circ\).
What is the difference between 180 and 360 degrees here?
Angles on a straight line make \(180^\circ\), a half turn. Angles all the way round a point make \(360^\circ\), a full turn.