Angles

Start by reading a protractor that is drawn for you, then move on to the rules that let you work out an angle you cannot measure.

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An angle is an amount of turn

Not a corner, and not how long the arms are. A quarter turn is 90° and we call it a right angle; half a turn is 180° and looks like a straight line; all the way round is 360°. Everything else in this topic comes from those three.

Three rules worth knowing by heart

  • On a straight line: 180°. Two angles sitting on a line always add to a half turn.
  • Around a point: 360°. Angles that meet at a point and fill the space add to a whole turn.
  • In a triangle: 180°. Always, for every triangle, however stretched or squashed it looks.

Mixing up the first two is the most common mistake here — 180 and 360 are easy to swap. It helps to picture the turn: a straight line is only halfway round.

Angles get turned too

A right angle drawn with one arm lying flat along the bottom is easy to spot. Rotate the whole thing and many people stop recognising it, because they learned the picture rather than the turn. So the angles here are drawn at all sorts of orientations.

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