Angles on a Line and at a Point
Angles fit together in two tidy ways. When several angles sit side by side along a
straight line, they always add up to 180^\circ — a
straight line is a "half turn". And when angles meet all the way around a point,
filling a full turn, they add up to 360^\circ.
\text{on a line} = 180^\circ \qquad \text{around a point} = 360^\circ
These two facts let you find a missing angle by subtraction — no protractor needed. They build on
measuring angles in degrees.
Two facts about angles that share a vertex:
-
angles on a straight line add up to 180^\circ —
if a and b lie on a line then
a + b = 180^\circ;
-
angles all the way around a point add up to
360^\circ — if x,
y and z fill the turn then
x + y + z = 360^\circ.
Why it works
A straight line is half of a full turn, and a full turn around a point is everything. Step through
both pictures.
So whenever angles sit on a line, fill in the missing one with 180^\circ - (\text{the rest});
around a point, use 360^\circ - (\text{the rest}).
Practise: chase the angles
Two lines cross at a point. Fill in every angle you can — using angles on a straight
line — ending with the highlighted one. Refresh for a new figure;
Check explains each step.