Angles that fill a straight line
Draw a line. Draw one ray going up from a point on it. How much do the two pieces add to?
- A straight line, cut by one ray, into two pieces.
- The two pieces add to 180°.
- Add another ray. Three pieces still add to 180°.
- Rays all round the point add to 360°.
The rule
The two pieces add to 180°. Each piece is an angle.
Angles side by side on a straight line add to exactly 180°. It does not matter how many pieces there are. Two side-by-side angles on a line are a linear pair. Two angles that add to 180° are also called supplementary angles.
Angles all the way round a point add to exactly 360°.
The 180° rule shows why vertically opposite angles are equal.
Two lines cross at one point. Name the four angles a, b, c, d.
| Step | What it gives |
|---|---|
| a + b = 180, one line | a = 180 − b |
| b + c = 180, the other line | c = 180 − b |
Both rows give 180 − b, so a = c.
Watch out!
"Two angles adding to 180° must sit on a straight line." Not true. Draw 110° in a notebook and 70° on a wall. They add to 180°. They share no point at all. The pieces must be side by side.
Pick line or point, then a size. Find x.
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