What stays the same?
On paper a pair of angles is one pair, and "they add to 180" is something you are told. Swing the arm here instead. The two numbers run in opposite directions through every value they can take, and the total sits there not moving.
125° + 55° = 180°
- This pair is
- Supplementary
- What holds
- they always total 180°
The figure
Drag the end of the arm round the point.
Ready to try some? Angle pair worksheets
Where it usually goes wrong
Complementary and supplementary get stored as two words to be told apart in an exam, and “they add to 180°” gets applied to any two angles that happen to be in the same picture. The total is fixed by the figure they sit in — a corner, a straight line, a crossing — and not by the angles themselves.
Try this
- Swing the arm and watch the two numbers run in opposite directions while the total does not move.
- Switch the figure from a straight line to a right angle. Same two angles, different total, and the word changes with it.
- Choose Two lines crossing and find the pair that stays equal rather than adding to anything.
Where this goes next
This is why one angle in a diagram is often enough to find five more, which is the whole method in angles in parallel lines.