
Constructing 75° 105° 120° 135° 150° angles and more
On other pages there are instructions for constructing angles of 30°, 45°, 60° and 90°.
By combining them you can construct other angles.
Adding angles
Angles can be effectively 'added' by constructing them so they share a side. This is
shown in
Constructing the sum of angles.
As an example, by first constructing a 30° angle and then a 45° angle, you will get a 75° angle.
The table below shows some angles that can be obtained by summing simpler ones in various ways
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.
Complementary and supplementary angles
By constructing the
supplementary angle
of a given angle, you get another one to combine as above. For example a 60° angle can be used to create a 120° angle by constructing its supplementary angle. This is shown in
Constructing a supplementary angle.
Similarly, you can find the complementary angle. For example the complementary angle for 20° is 70°.
Finding the complementary angle is shown in
Constructing a complementary angle.
The basic constructions are described on these pages:
Constructions pages on this site
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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