construction of angles like 60 degree, 30 degree, 90 degree, 120 degree, 45 degree construction of angle bisector

1. Construction of basic angles

2. Construct 60 degree angle
Construct AB line
Draw arc of random radius from A
Let D be point of intersection of arc and line
With same radius cut the arc from D
Let point of intersection of both arcs be M
Join MA
Angle MAD = 60 degree A
B
D
M

3. Construct 120 degree angle
Construct AB line
Draw arc of random radius from A
Let D be point of intersection of arc and line
With same radius cut the arc from D
Let point of intersection of both arcs be M
From M, again cut the arc of same radius on previous arc
Let the point of intersection be N
Join NA
So angle NAD is 120 degree
A B
D
M
N

4. Construct 90 degree angle
Construct AB line
Draw arc of random radius from A
Let D be point of intersection of arc and line
With same radius cut the arc from D
Let point of intersection of both arcs be M
From M, again cut the arc of same radius on previous arc
Let the point of intersection be N
From N and M draw arcs of equal radius and intersect them at X
Join AX. Angle XAD is 90 degree
A B
D
M
N
X

5. Construct angle bisector of any random angle.
Make any random angle CAB
From A construct arc between C and B
Name point of intersection as M and N
From M and N construct two arcs intersecting
each other as shown. Let intersection point be Y.
Join A and Y
So angle CAB is divided in two equal parts CAY and YAB
A B
C
M
N
Y

6. Construct 30 degree angle
Make angle CAB equal to 60 degree as explained earlier.
From M and N construct two arcs as shown.
Let the point of intersection of both arcs be Y
Join AY
Angle YAB will be 30 degree
A B
C
M
N
Y

7. Construct 45 degree angle
Construct 90 as explained earlier
Mark point C as shown in figure.
From point C and D construct two
intersecting arcs of equal radius.
Let intersecting point be Y.
Join AY
Angle YAD will be 45 degree.
A B
D
M
N
X
C
Y

8. For constructing 135 degree, construct bisector of angle between 90
degree and 180 degree
For constructing 150 degree, construct bisector of angle between 120
and 180 degree
For 75 degree, bisect the angle between 60 and 90
For 105 bisect the angle between 90 and 120