The document describes steps for performing operations with angles using a compass. It includes copying an angle onto a new ray, drawing the bisector of an angle, and carrying out calculations by adding, subtracting and combining angles. For example, it shows how to add angles A and B by copying each angle onto a ray and combining the arcs, and how to subtract angle A from angle B by copying B, then copying A inside it and removing the overlapping region.

1. OPERATIONS WITH ANGLES

2. Exercise 1
Given the angle A, copy it onto the ray from V´

3. We have the angle A, that
we want to copy onto the
ray from V´

4. STEPS:
1.Centering at V, we draw an arc (no matter
the length you take with the compass).
You get the points 1 and 2

5. STEPS:
1.Centering at V, we draw an arc (no matter
the length you take with the compass).
You get the points 1 and 2

6. STEPS:
1.Centering at V, we draw an arc (no matter
the length you take with the compass).
You get the points 1 and 2

7. STEPS:
2.With the same length in the compass, we
draw the same arc from V´ getting the point 1

8. STEPS:
2.With the same length in the compass, we
draw the same arc from V´ getting the point 1

9. STEPS:
2.With the same length in the compass, we
draw the same arc from V´ getting the point 1

10. STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1

11. STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1

12. STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1

13. STEPS:
3.Now we take the distance 1-2 from the given arc and
we transport it to the new one, from the point 1

14. STEPS:
4.We get the point 2. Joining the vertex V´ and the
point 2 we obtain the angle copied.

15. STEPS:
4.We get the point 2. Joining the vertex V´ and the
point 2 we obtain the angle copied.

16. Exercise 2
Draw the bisector of the given angle A

17. We have the angle A and
we want to draw the
bisector of this angle

18. STEPS:
1.Centering at the vertex, we draw an arc
(no matter the length you take with the
compass). You get the points 1 and 2

19. STEPS:
1.Centering at the vertex, we draw an arc
(no matter the length you take with the
compass). You get the points 1 and 2

20. STEPS:
1.Centering at the vertex, we draw an arc
(no matter the length you take with the
compass). You get the points 1 and 2

21. STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length

22. STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length

23. STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length

24. STEPS:
2.Centering at each point and opening the
compass further than the middle, draw
two arcs with the same length

25. STEPS:
3.Where the two arcs intersect , join it with
the vertex and you obtain the bisector of
the angle

26. Exercise 3
Given the following angles A, B and C, carry out
the requested operations

27. Exercise 3
angle A + angle B

28. We have to add the angle
A and the angle B

29. STEPS:
1.We have to copy the angle A
onto the ray as we saw
before. To do so, we are
going to draw the same arc
in all of them

30. STEPS:
1.We have to copy the angle A
onto the ray as we saw
before. To do so, we are
going to draw the same arc
in all of them

31. STEPS:
2.In the first angle, we get the
points 1 and 2

32. STEPS:
3.In the second angle, we get
the points 3 and 4

33. STEPS:
3.In the second angle, we get
the points 3 and 4

34. STEPS:
3.In the second angle, we get
the points 3 and 4

35. STEPS:
4.In the third angle, we get
the points 5 and 6

36. STEPS:
4.In the third angle, we get
the points 5 and 6

37. STEPS:
4.In the third angle, we get
the points 5 and 6

38. STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle

39. STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle

40. STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle

41. STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle

42. STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle

43. STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle

44. STEPS:
5.Now, we copy the first angle
onto the ray. To do it, we
draw the same arc and we
obtain the point 1. Then, on
this arc we transport the
distance 1-2 of the original
angle

45. STEPS:
7.We join the point 2 with the
vertex V´and we have the
angle A copied

46. STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc

47. STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc

48. STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc

49. STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc

50. STEPS:
7.Now, we have to copy the
angle B outside the angle A.
To do so, we have to take
the distance 3-4 from the
angle B and transport it
onto the same arc

51. STEPS:
8.The result is the space
marked in light pink color

52. Exercise 3
angle B – angle A

53. We have to substract to
the angle B, the angle A

54. STEPS:
1.We have to copy first the
angle B onto the ray and
then, copy the angle A
inside the angle B

55. STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray

56. STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray

57. STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray

58. STEPS:
2.We have to transport the
distance 3-4 of the angle B
onto the ray

59. STEPS:
3.Join the vertex 4
with the vertex V´
and you get the
angle B copied

60. STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B

61. STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B

62. STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B

63. STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B

64. STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B

65. STEPS:
4.Now, we have to
copy the angle A
inside the angle B.
To do so, we have
to transport the
distance 1-2 of the
angle A inside the
angle B

66. STEPS:
5.The result of the
operation is the
space marked in
light pink color

67. Exercise 3
angle B + angle C – angle A

68. We have to do two
operations. First we have
to add the angles B and C
and then, substract with
the result, the angle A

69. STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray

70. STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray

71. STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray

72. STEPS:
1.We have to copy first the
angle B. So, we have to
transport the distance 3-4
onto the ray

73. STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B

74. STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B

75. STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B

76. STEPS:
2.Once we get the
angle B we have
to add it the
angle C. So, we
have to transport
the distance 5-6
outward the
angle B

77. STEPS:
2.Once we get the
addittion of the
angles B and C,
we have to
substract the
angle A to the
result.

78. STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation

79. STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation

80. STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation

81. STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation

82. STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation

83. STEPS:
3.So, we have to
transport the
distance 1-2 of the
angle A inward the
result of the
previous operation

84. STEPS:
4.The result is the
space marked in
light pink color