Constructions: 60, 30 and 45 Degree Angles
Constructing a 60 Degree Angle:
To construct a 60 degree angle, you use similar methods as constructing an
equilateral triangle.
1) On the line below, using a compass and
a straight edge, construct a 60 degree
angle at A.
2) Construct a 60 degree angle whose
vertex is at P
. P
A
B
3) Using a straight edge and a compass on
the diagram of UF , construct an angle
of 60 degrees whose vertex is at point F
4) Using a compass, a straight edge and
ET below, create EL to make an angle
of 60 degrees.
E
U
F
T
Constructing a 30 Degree Angle:
To construct a 30 degree angle, you use similar methods as constructing an
equilateral triangle then you must bisect that angle.
1) Using a compass, a straight edge, create
an angle whose measure is 30 degrees.
2) Construct a 30 degree angle whose
vertex is at Q
. Q
3) Using a straight edge and a compass on
the diagram of AB , construct an angle
of 30 degrees whose vertex is at point F
4) On the line below, using a compass and
a straight edge, construct a 30 degree
angle at Y.
B
A
X
Y
Constructing a 45 Degree Angle:
To construct a 45 degree angle, you must construct a perpendicular line and then
bisect the right angle that you created.
1) Using a compass and a straight edge,
construct a 45 degree angle.
3) Construct a 45 degree angle whose
vertex is at Q
2) Construct a 45 degree angle at point A
A
B
4) Using a straight edge and a compass on
the diagram of XY , construct an angle
of 45 degrees whose vertex is at point Y
X
Y
. Q