1. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Angles and Lines
Matem´ticas 1o E.S.O.
a
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2. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
1 Lines
2 Perpendicular bisector of a segment and bisector of an angle
3 Sexagesimal system and angles
4 Sexagesimal system and time
5 Adding and Subtracting in the sexagesimal system
6 Exercises
Angles and Lines

3. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Lines
Angles and Lines

4. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Lines
Plane Geometry
Plane Geometry deals with figures in a plane (circles, lines,
polygons. . . )
A line is a set of points extending in two opposite directions
without end, It’s a straight one-dimensional figure with no
thickness and extending infinitely in both directions. A line is
sometimes called a straight line. Points are said to be collinear
points if they lie on a single straight line. A plane is a flat surface
that has no thickness and extends without ending in ALL
directions.
Points are said to be coplanar points if
they lie on a common plane.
A line segment is a finite portion of an
infinite line. A line segment always has
a beginning and an end.
Angles and Lines

5. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Lines
Plane Geometry
Plane Geometry deals with figures in a plane (circles, lines,
polygons. . . )
A line is a set of points extending in two opposite directions
without end, It’s a straight one-dimensional figure with no
thickness and extending infinitely in both directions. A line is
sometimes called a straight line. Points are said to be collinear
points if they lie on a single straight line. A plane is a flat surface
that has no thickness and extends without ending in ALL
directions.
Points are said to be coplanar points if
they lie on a common plane.
A line segment is a finite portion of an
infinite line. A line segment always has
a beginning and an end.
Angles and Lines

6. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Lines
Perpendicular bisector of a segment and bisector of an
angle
Lines that intersect in a point are called intersecting lines. Lines
that do not intersect are called parallel lines (in the plane). Two
lines that lie on top of one another are called coincident lines.
Two lines or line segments which are perpendicular are said to be
orthogonal (two lines are said to be perpendicular if they meet at a
90o angle).
Given two intersecting lines, the point
of intersection is called the vertex
and the amount of rotation about the
vertex required to bring one line into
correspondence with the other is called
the angle between them.
Angles and Lines

7. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Lines
One full rotation corresponds to 360 degrees.
Half a full rotation is called a straight angle, and a quarter of a full
rotation is called a right angle.
An angle less than a right angle is called an acute angle, an angle
greater than a right angle (but less than a straight angle) is called
an obtuse angle, and an angle greater than a straight angle (but
less than a full angle) is called a reflex angle.
Angles and Lines

8. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Perpendicular bisector of a
segment and bisector of an
angle
Angles and Lines

9. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Perpendicular bisector of a segment and bisector of an angle
Bisector of a line segment
A perpendicular bisector of a line segment AB is a line
perpendicular to AB and passing through the midpoint M of AB.
Angles and Lines

10. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Perpendicular bisector of a segment and bisector of an angle
Bisector of an angle
The bisector of an angle is the line that divides the angle into
two equal parts.
Angles and Lines

11. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and angles
Angles and Lines

12. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and angles
The size of an angle
There are several ways to measure the size of an angle, for example
using units of degrees: In a complete circle there are three hundred
and sixty degrees. You can express angles to any precision using
decimal numbers.
Example: 30 degrees and a half is 30.5 degrees.
There is another way to state the size of an angle, subdividing a
degree. The degree is divided into sixty parts called minutes. These
minutes are further divided into sixty parts called seconds.
Angles and Lines

13. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and angles
The size of an angle
There are several ways to measure the size of an angle, for example
using units of degrees: In a complete circle there are three hundred
and sixty degrees. You can express angles to any precision using
decimal numbers.
Example: 30 degrees and a half is 30.5 degrees.
There is another way to state the size of an angle, subdividing a
degree. The degree is divided into sixty parts called minutes. These
minutes are further divided into sixty parts called seconds.
Angles and Lines

14. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and angles
Angles: Degrees, minutes and seconds
In a full circle there are 360 degrees, each degree is split up into 60
parts called minutes (each part being 1/60 of a degree), each
minute is split up into 60 parts called seconds (each part being
1/60 of a minute).
Example: 40 degrees, 20 minutes and 50 seconds is usually written
this way: 40o 20 50 .
Example: 30.5 degrees is 30o and 30 , because 0.5 degrees are
0.5 · 60 = 30 minutes.
Angles and Lines

15. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and angles
Angles: Degrees, minutes and seconds
In a full circle there are 360 degrees, each degree is split up into 60
parts called minutes (each part being 1/60 of a degree), each
minute is split up into 60 parts called seconds (each part being
1/60 of a minute).
Example: 40 degrees, 20 minutes and 50 seconds is usually written
this way: 40o 20 50 .
Example: 30.5 degrees is 30o and 30 , because 0.5 degrees are
0.5 · 60 = 30 minutes.
Angles and Lines

16. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and time
Angles and Lines

17. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and time
Time: Hours, minutes and seconds
To measure time we can use hours: In a day there are twenty-four
hours. You can express time to any precision using decimal
numbers.
Example: 3 hours and a quarter is 3.25 hours.
There is another way to state the amount of time, subdividing an
hour. The hour is divided into sixty parts called minutes. These
minutes are further divided into sixty parts called seconds.
In a day there are 24 hours, each hour is split up into 60 parts
called minutes (each part being 1/60 of an hour), each minute is
split up into 60 parts called seconds (each part being 1/60 of a
minute).
Example: 14 hours, 56 minutes and 12 seconds is usually written
this way: 14 hr 56 min 12 sec.
Example: 3.25 hours is 3 hr and 15 min, because 0.25 hours are
0.25 · 60 = 15 minutes.
Angles and Lines

18. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and time
Time: Hours, minutes and seconds
To measure time we can use hours: In a day there are twenty-four
hours. You can express time to any precision using decimal
numbers.
Example: 3 hours and a quarter is 3.25 hours.
There is another way to state the amount of time, subdividing an
hour. The hour is divided into sixty parts called minutes. These
minutes are further divided into sixty parts called seconds.
In a day there are 24 hours, each hour is split up into 60 parts
called minutes (each part being 1/60 of an hour), each minute is
split up into 60 parts called seconds (each part being 1/60 of a
minute).
Example: 14 hours, 56 minutes and 12 seconds is usually written
this way: 14 hr 56 min 12 sec.
Example: 3.25 hours is 3 hr and 15 min, because 0.25 hours are
0.25 · 60 = 15 minutes.
Angles and Lines

19. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Sexagesimal system and time
Time: Hours, minutes and seconds
To measure time we can use hours: In a day there are twenty-four
hours. You can express time to any precision using decimal
numbers.
Example: 3 hours and a quarter is 3.25 hours.
There is another way to state the amount of time, subdividing an
hour. The hour is divided into sixty parts called minutes. These
minutes are further divided into sixty parts called seconds.
In a day there are 24 hours, each hour is split up into 60 parts
called minutes (each part being 1/60 of an hour), each minute is
split up into 60 parts called seconds (each part being 1/60 of a
minute).
Example: 14 hours, 56 minutes and 12 seconds is usually written
this way: 14 hr 56 min 12 sec.
Example: 3.25 hours is 3 hr and 15 min, because 0.25 hours are
0.25 · 60 = 15 minutes.
Angles and Lines

20. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the
sexagesimal system
Angles and Lines

21. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Add in the sexagesimal system
You must add or subtract the units separately. But you may need to
do some adjusting if the hours end up 24 or more, the minutes end
up 60 or more, the seconds end up 60 or more,or less than zero.
Adding
Add the hours. If the hours are 24 or more, subtract 24 from the
hours and add 1 to the days. Add the minutes. If the minutes are
60 or more, subtract 60 from the hours and add 1 to the hours.
And so on.
Example: 40o 20 50 + 10o 33 6 = 50o 55 56 .
Example: 14 hr 20 min 50 sec + 15 hr 43 min 26 sec
=29 hr 63 min 76 sec =1 day 6 hr 4 min 16 sec.
Angles and Lines

22. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Add in the sexagesimal system
You must add or subtract the units separately. But you may need to
do some adjusting if the hours end up 24 or more, the minutes end
up 60 or more, the seconds end up 60 or more,or less than zero.
Adding
Add the hours. If the hours are 24 or more, subtract 24 from the
hours and add 1 to the days. Add the minutes. If the minutes are
60 or more, subtract 60 from the hours and add 1 to the hours.
And so on.
Example: 40o 20 50 + 10o 33 6 = 50o 55 56 .
Example: 14 hr 20 min 50 sec + 15 hr 43 min 26 sec
=29 hr 63 min 76 sec =1 day 6 hr 4 min 16 sec.
Angles and Lines

23. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Add in the sexagesimal system
You must add or subtract the units separately. But you may need to
do some adjusting if the hours end up 24 or more, the minutes end
up 60 or more, the seconds end up 60 or more,or less than zero.
Adding
Add the hours. If the hours are 24 or more, subtract 24 from the
hours and add 1 to the days. Add the minutes. If the minutes are
60 or more, subtract 60 from the hours and add 1 to the hours.
And so on.
Example: 40o 20 50 + 10o 33 6 = 50o 55 56 .
Example: 14 hr 20 min 50 sec + 15 hr 43 min 26 sec
=29 hr 63 min 76 sec =1 day 6 hr 4 min 16 sec.
Angles and Lines

24. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Add in the sexagesimal system
You must add or subtract the units separately. But you may need to
do some adjusting if the hours end up 24 or more, the minutes end
up 60 or more, the seconds end up 60 or more,or less than zero.
Adding
Add the hours. If the hours are 24 or more, subtract 24 from the
hours and add 1 to the days. Add the minutes. If the minutes are
60 or more, subtract 60 from the hours and add 1 to the hours.
And so on.
Example: 40o 20 50 + 10o 33 6 = 50o 55 56 .
Example: 14 hr 20 min 50 sec + 15 hr 43 min 26 sec
=29 hr 63 min 76 sec =1 day 6 hr 4 min 16 sec.
Angles and Lines

25. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Subtract in the sexagesimal system
Subtracting
Subtract the hours. If the hours are negative, add 24 to the hours
and subtract 1 from days. Subtract the minutes. If the minutes are
negative, add 60 to the minutes and subtract 1 from hours. And so
on.
Example: 23 hr 40 min 51 sec − 15 hr 33 min 21 sec =
8 hr 7 min 30 sec.
Example:
45o 33 12 −11o 42 20 =44o 92 72 −11o 42 20 =33o 50 52 .
Angles and Lines

26. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Subtract in the sexagesimal system
Subtracting
Subtract the hours. If the hours are negative, add 24 to the hours
and subtract 1 from days. Subtract the minutes. If the minutes are
negative, add 60 to the minutes and subtract 1 from hours. And so
on.
Example: 23 hr 40 min 51 sec − 15 hr 33 min 21 sec =
8 hr 7 min 30 sec.
Example:
45o 33 12 −11o 42 20 =44o 92 72 −11o 42 20 =33o 50 52 .
Angles and Lines

27. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Subtract in the sexagesimal system
Subtracting
Subtract the hours. If the hours are negative, add 24 to the hours
and subtract 1 from days. Subtract the minutes. If the minutes are
negative, add 60 to the minutes and subtract 1 from hours. And so
on.
Example: 23 hr 40 min 51 sec − 15 hr 33 min 21 sec =
8 hr 7 min 30 sec.
Example:
45o 33 12 −11o 42 20 =44o 92 72 −11o 42 20 =33o 50 52 .
Angles and Lines

28. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Subtract in the sexagesimal system
Subtracting
Subtract the hours. If the hours are negative, add 24 to the hours
and subtract 1 from days. Subtract the minutes. If the minutes are
negative, add 60 to the minutes and subtract 1 from hours. And so
on.
Example: 23 hr 40 min 51 sec − 15 hr 33 min 21 sec =
8 hr 7 min 30 sec.
Example:
45o 33 12 −11o 42 20 =44o 92 72 −11o 42 20 =33o 50 52 .
Angles and Lines

29. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Adding and Subtracting in the sexagesimal system
Subtract in the sexagesimal system
Subtracting
Subtract the hours. If the hours are negative, add 24 to the hours
and subtract 1 from days. Subtract the minutes. If the minutes are
negative, add 60 to the minutes and subtract 1 from hours. And so
on.
Example: 23 hr 40 min 51 sec − 15 hr 33 min 21 sec =
8 hr 7 min 30 sec.
Example:
45o 33 12 −11o 42 20 =44o 92 72 −11o 42 20 =33o 50 52 .
Angles and Lines

30. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Angles and Lines

31. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 1
Find five objects in your classroom that have right angles:
Angles and Lines

32. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 1
Find five objects in your classroom that have right angles:
Angles and Lines

33. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 2
Using the set square, draw an angle of a)45o b)30o c)105o d)15o
Angles and Lines

34. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 2
45o 30o
105o 15o
Angles and Lines

35. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 3
For each angle below, state whether the angle is acute, obtuse or
reflex:
Angles and Lines

36. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 3
For each angle below, state whether the angle is acute, obtuse or
reflex:
Angles and Lines

37. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 4
Measure the following angles:
Angles and Lines

38. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 4
Measure the following angles:
Angles and Lines

39. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 6
Write down the following amounts:
1 43o 34 25 :
2 5o 17 30 :
3 3 hr 14 min 18 sec:
4 15 hr 56 min 24 sec:
Angles and Lines

40. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 6
Write down the following amounts:
1 43o 34 25 : forty degrees, twenty minutes and fifty
seconds.
2 5o 17 30 : five degrees, seventeen minutes and thirty
seconds.
3 3 hr 14 min 18 sec: three hours, fourteen minutes and
eighteen seconds.
4 15 hr 56 min 24 sec: fifteen hours, fifty-eight minutes
and twenty-four seconds.
Angles and Lines

41. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 6
Write down the following amounts:
1 43o 34 25 : forty degrees, twenty minutes and fifty
seconds.
2 5o 17 30 : five degrees, seventeen minutes and thirty
seconds.
3 3 hr 14 min 18 sec: three hours, fourteen minutes and
eighteen seconds.
4 15 hr 56 min 24 sec: fifteen hours, fifty-eight minutes
and twenty-four seconds.
Angles and Lines

42. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 6
Write down the following amounts:
1 43o 34 25 : forty degrees, twenty minutes and fifty
seconds.
2 5o 17 30 : five degrees, seventeen minutes and thirty
seconds.
3 3 hr 14 min 18 sec: three hours, fourteen minutes and
eighteen seconds.
4 15 hr 56 min 24 sec: fifteen hours, fifty-eight minutes
and twenty-four seconds.
Angles and Lines

43. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 6
Write down the following amounts:
1 43o 34 25 : forty degrees, twenty minutes and fifty
seconds.
2 5o 17 30 : five degrees, seventeen minutes and thirty
seconds.
3 3 hr 14 min 18 sec: three hours, fourteen minutes and
eighteen seconds.
4 15 hr 56 min 24 sec: fifteen hours, fifty-eight minutes
and twenty-four seconds.
Angles and Lines

44. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 6
Write down the following amounts:
1 43o 34 25 : forty degrees, twenty minutes and fifty
seconds.
2 5o 17 30 : five degrees, seventeen minutes and thirty
seconds.
3 3 hr 14 min 18 sec: three hours, fourteen minutes and
eighteen seconds.
4 15 hr 56 min 24 sec: fifteen hours, fifty-eight minutes
and twenty-four seconds.
Angles and Lines

45. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 7
Find:
1 34o 14 15 + 11o 13 15 =
2 55o 44 52 + 24o 53 34 =
3 3 hr 34 min 17 sec + 4 hr 11 min 34 sec =
4 18 hr 34 min 37 sec + 12 hr 26 min 34 sec =
Angles and Lines

46. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 7
Find:
1 34o 14 15 + 11o 13 15 =45o 27 30
2 55o 44 52 + 24o 53 34 =80o 38 26
3 3 hr 34 min 17 sec +
4 hr 11 min 34 sec =7 hr 45 min 51 sec
4 18 hr 34 min 37 sec +
12 hr 26 min 34 sec =1 day 7 hr 1 min 11 sec
Angles and Lines

47. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 7
Find:
1 34o 14 15 + 11o 13 15 =45o 27 30
2 55o 44 52 + 24o 53 34 =80o 38 26
3 3 hr 34 min 17 sec +
4 hr 11 min 34 sec =7 hr 45 min 51 sec
4 18 hr 34 min 37 sec +
12 hr 26 min 34 sec =1 day 7 hr 1 min 11 sec
Angles and Lines

48. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 7
Find:
1 34o 14 15 + 11o 13 15 =45o 27 30
2 55o 44 52 + 24o 53 34 =80o 38 26
3 3 hr 34 min 17 sec +
4 hr 11 min 34 sec =7 hr 45 min 51 sec
4 18 hr 34 min 37 sec +
12 hr 26 min 34 sec =1 day 7 hr 1 min 11 sec
Angles and Lines

49. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 7
Find:
1 34o 14 15 + 11o 13 15 =45o 27 30
2 55o 44 52 + 24o 53 34 =80o 38 26
3 3 hr 34 min 17 sec +
4 hr 11 min 34 sec =7 hr 45 min 51 sec
4 18 hr 34 min 37 sec +
12 hr 26 min 34 sec =1 day 7 hr 1 min 11 sec
Angles and Lines

50. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 7
Find:
1 34o 14 15 + 11o 13 15 =45o 27 30
2 55o 44 52 + 24o 53 34 =80o 38 26
3 3 hr 34 min 17 sec +
4 hr 11 min 34 sec =7 hr 45 min 51 sec
4 18 hr 34 min 37 sec +
12 hr 26 min 34 sec =1 day 7 hr 1 min 11 sec
Angles and Lines

51. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 8
Find:
1 45o 21 45 − 33o 12 15 =
2 53o 24 12 − 32o 43 44 =
3 6 hr 24 min 15 sec − 4 hr 1 min 5 sec =
4 8 hr 24 min 13 sec − 5 hr 25 min 36 sec =
Angles and Lines

52. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 8
Find:
1 45o 21 45 − 33o 12 15 =12o 9 30
2 53o 24 12 − 32o 43 44 =20o 40 26
3 6 hr 24 min 15 sec −
4 hr 1 min 5 sec =2 hr 23 min 10sec
4 8 hr 24 min 13 sec −
5 hr 25 min 36 sec =2 hr 58 min 37sec
Angles and Lines

53. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 8
Find:
1 45o 21 45 − 33o 12 15 =12o 9 30
2 53o 24 12 − 32o 43 44 =20o 40 26
3 6 hr 24 min 15 sec −
4 hr 1 min 5 sec =2 hr 23 min 10sec
4 8 hr 24 min 13 sec −
5 hr 25 min 36 sec =2 hr 58 min 37sec
Angles and Lines

54. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 8
Find:
1 45o 21 45 − 33o 12 15 =12o 9 30
2 53o 24 12 − 32o 43 44 =20o 40 26
3 6 hr 24 min 15 sec −
4 hr 1 min 5 sec =2 hr 23 min 10sec
4 8 hr 24 min 13 sec −
5 hr 25 min 36 sec =2 hr 58 min 37sec
Angles and Lines

55. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 8
Find:
1 45o 21 45 − 33o 12 15 =12o 9 30
2 53o 24 12 − 32o 43 44 =20o 40 26
3 6 hr 24 min 15 sec −
4 hr 1 min 5 sec =2 hr 23 min 10sec
4 8 hr 24 min 13 sec −
5 hr 25 min 36 sec =2 hr 58 min 37sec
Angles and Lines

56. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 8
Find:
1 45o 21 45 − 33o 12 15 =12o 9 30
2 53o 24 12 − 32o 43 44 =20o 40 26
3 6 hr 24 min 15 sec −
4 hr 1 min 5 sec =2 hr 23 min 10sec
4 8 hr 24 min 13 sec −
5 hr 25 min 36 sec =2 hr 58 min 37sec
Angles and Lines

57. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 9
Luis is a marathon runner. He trains two days: on the first day he
runs the marathon in 2 hr 48 min 35 sec; and on the second day
he runs it in 2 hr 45 min 30 sec. How long does Luis run over the
two days in total?
Angles and Lines

58. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 9
Luis is a marathon runner. He trains two days: on the first day he
runs the marathon in 2 hr 48 min 35 sec; and on the second day
he runs it in 2 hr 45 min 30 sec. How long does Luis run over the
two days in total?
Data: First day:
2 hr 48 min 35 sec
Second day:
2 hr 45 min 30 sec
2 hr 48 min 35 sec
+ 2 hr 45 min 30 sec
Answer: Luis runs
5 hr 34 min 5 sec 5 hr 34 min 5 sec in
total.
Angles and Lines

59. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 9
Luis is a marathon runner. He trains two days: on the first day he
runs the marathon in 2 hr 48 min 35 sec; and on the second day
he runs it in 2 hr 45 min 30 sec. How long does Luis run over the
two days in total?
Data: First day:
2 hr 48 min 35 sec
Second day:
2 hr 45 min 30 sec
2 hr 48 min 35 sec
+ 2 hr 45 min 30 sec
Answer: Luis runs
5 hr 34 min 5 sec 5 hr 34 min 5 sec in
total.
Angles and Lines

60. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 9
Luis is a marathon runner. He trains two days: on the first day he
runs the marathon in 2 hr 48 min 35 sec; and on the second day
he runs it in 2 hr 45 min 30 sec. How long does Luis run over the
two days in total?
Data: First day:
2 hr 48 min 35 sec
Second day:
2 hr 45 min 30 sec
2 hr 48 min 35 sec
+ 2 hr 45 min 30 sec
Answer: Luis runs
5 hr 34 min 5 sec 5 hr 34 min 5 sec in
total.
Angles and Lines

61. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 9
Luis is a marathon runner. He trains two days: on the first day he
runs the marathon in 2 hr 48 min 35 sec; and on the second day
he runs it in 2 hr 45 min 30 sec. How long does Luis run over the
two days in total?
Data: First day:
2 hr 48 min 35 sec
Second day:
2 hr 45 min 30 sec
2 hr 48 min 35 sec
+ 2 hr 45 min 30 sec
Answer: Luis runs
5 hr 34 min 5 sec 5 hr 34 min 5 sec in
total.
Angles and Lines

62. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 10
Ana spent 7 hr 20 min 28 sec on painting a room in the weekend.
She worked the same amount of time each day. How much time
did she work each day?
Angles and Lines

63. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 10
Ana spent 7 hr 20 min 28 sec on painting a room in the weekend.
She worked the same amount of time each day. How much time
did she work each day?
Data: She Ana spent
7 hr 20 min 28 sec
1 hr 40 min 14 sec
+ 1 hr 40 min 14 sec
Answer: She worked
3 hr 20 min 28 sec 1 hr 40 min 14 sec a
day.
Angles and Lines

64. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 10
Ana spent 7 hr 20 min 28 sec on painting a room in the weekend.
She worked the same amount of time each day. How much time
did she work each day?
Data: She Ana spent
7 hr 20 min 28 sec
1 hr 40 min 14 sec
+ 1 hr 40 min 14 sec
Answer: She worked
3 hr 20 min 28 sec 1 hr 40 min 14 sec a
day.
Angles and Lines

65. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 10
Ana spent 7 hr 20 min 28 sec on painting a room in the weekend.
She worked the same amount of time each day. How much time
did she work each day?
Data: She Ana spent
7 hr 20 min 28 sec
1 hr 40 min 14 sec
+ 1 hr 40 min 14 sec
Answer: She worked
3 hr 20 min 28 sec 1 hr 40 min 14 sec a
day.
Angles and Lines

66. Indice Lines Bisectors Sexagesimal system and angles Sexagesimal system and time Adding and Subtracting Exercises
Exercises
Exercise 10
Ana spent 7 hr 20 min 28 sec on painting a room in the weekend.
She worked the same amount of time each day. How much time
did she work each day?
Data: She Ana spent
7 hr 20 min 28 sec
1 hr 40 min 14 sec
+ 1 hr 40 min 14 sec
Answer: She worked
3 hr 20 min 28 sec 1 hr 40 min 14 sec a
day.
Angles and Lines