Furthermore, by combining three angles many more can be constructed.
You can subtract them too
By constructing an angle "inside" another you can effectively subtract them.
So if you started with a 70° angle and constructed a 45° angle inside it sharing a side, the result would be a 25° angle.
This is shown in the construction
Constructing the difference between two angles
Bisecting an angle 'halves' it
By bisecting an angle you get two angles of half the measure of the first.
This gives you some more angles to combine as described above.
For example constructing a 30° angle and then bisecting it you get two 15° angles.
Bisection is shown in
Bisecting an Angle.