Math exercises

1. Angles
Grade 7– Mathematics

2. • An angle is defined as the amount of turn
between two rays that share a common
end point.
• Angles are measured in degrees
Angles 90
°

3. Let’s identify the
parts of an
angle!
T X

4. Let’s identify the
parts of an
angle!
V E R T E X

5. Let’s identify the
parts of an
angle!
R

6. Let’s identify the
parts of an
angle!
A RM S

7. Let’s identify the
parts of an
angle!
D G

8. Let’s identify the
parts of an
angle!
D E G R E E S

9. the common
point where
the two rays
meet
vertex
the rays that
make up the
angle
arms
the measure
of the size of
an angle
degrees

10. Naming Angles
1
One way is to use
the ∠symbol followed
by three letters.
The first and third
letters indicate points
on the two arms.
The letter in the middle
is the vertex.
A B C
∠
∠
C B A

11. Naming Angles
using the ∠symbol
only with the vertex
point.
The angle would
be called ∠B.
by using the ∠symbol
followed by the letter
or number between
the angle.
Thiswould be ∠
1.
1
∠ABC
∠CBA
∠CAB
∠BCA
∠B ∠1

12. 4 5
?
?
?
?
?
?
?
?
?

13. Kinds of Angles
acute
angle
less than 90°
obtuse
angle
more than 90°
less than 180°
right
angle
exactly to 90°

14. Kinds of Angles
reflex
angle
more than 180°
Full
rotation
exactly 360°
straight
angle
exactly to 180°

15. acute right
obtuse straight

16. Protractor
A tool that is used to measure angles.
oute
r
scal
e
inne
r
scal
e
cente
r

17. Measuring Angles
Place the center of the protractor on the vertex B
A
B C

18. Measuring Angles
Place the center of the protractor on the vertex B
A
B C
Adjust the 0° baseline of the protractor so that it lines
up with line BC

19. Measuring Angles
B C
Place the center of the protractor on the vertex B
Adjust the 0° baseline of the protractor so that it lines
up with line BC
Since the angle is acute and the 0° line or baseline was used
from the right, you will take the reading from the inner scale
A
30°

20. Measuring Angles

21. Measuring Angles

22. Measuring Angles

23. Measuring Angles

24. Let’s Review!
These are angles whose
measure is exactly 90°
acute
right
obtuse
straight

25. Let’s Review!
(90° + 45°) is what
kind of angle?
acute
right
obtuse
straight

26. Let’s Review!
It is the sum of
two right angles.
acute
right
obtuse
straight

27. Let’s Review!
These are the rays that
make up the angle.
degrees
points
arms
vertex

28. Let’s Review!
It is the common point
where the two rays meet.
degrees
points
arms
vertex

29. Let’s Review!
It is the measure of
the size of an angle
degrees
points
arms
vertex

30. Let’s Review!
If the points A and Bare the arms,
what is the name of the angle if
point Cis the vertex?
∠ABC
∠BAC
∠CBA
∠ACB

31. Let’s Review!
How many ways
can you name the
angles on this
picture?
9
12
10
13

32. Let’s work together!
It is the only animal
that have fingerprints.
5 3 2 4 1
A – 20°
D – 60°
E – 35°
G – 110°
K – 155°
L – 120°
N – 160°
O – 145°
P – 25°

33. Let’s work together!
It is the only animal
that have fingerprints.
K O A L A
5 3 2 4 1
A – 20°
D – 60°
E – 35°
G – 110°
K – 155°
L – 120°
N – 160°
O – 145°
P – 25°

34. What is the measure of the angle?
20°

35. 20°
What is the measure of the angle?

36. 145°
What is the measure of the angle?

37. Assignment
Draw the next angles (use a protractor):
45°
60°
90°
150°
80°

38. Practice 4.4
Complete the chart.
Type of angle Measure of angle
Right angle 900
Acute angle Contains less than 900
Obtuse angle Contains more than 900 but
less than 1800
Straight 1800
Reflex angle Contains more than 1800 but
less than 3600

39. Practice 4.4
Name each angle (a) by its vertex and
(b) by three leters.
a. < Y
b. <XYZ or <ZYX
a. < K
b. <JKL or <LKJ
a. < S
b. <RST or <TSR
a. < E
b. <DEF or <FED

40. Practice 4.4
Find the complementary and
supplementary of each angle.
10.
a. Complementary angles= 900
<R= 300
90-30= 600
b. Supplementary angles =1800
180-30= 500
11.
a. Complementary angles= 900
<Y= 120
90-12= 780
b. Supplementary angles =1800
180-12= 1680

41. Practice 4.4
Find the complementary and
supplementary of each angle.
12.
a. Complementary angles= 900
<J= 610
90-61= 290
b. Supplementary angles =1800
180-61= 1190
13.
a. Complementary angles= 900
<M= 450
90-45= 450
b. Supplementary angles =1800
180-45= 1350

42. Practice 4.4
Determine if each pair of angles is
complentary, supplementary or neither.
14.
<Q= 200
<X= 700
Complementary angle
15.
<D= 1200
<X= 400
160
Neither

43. Practice 4.4
Determine if each pair of angles is
complentary, supplementary or neither.
16.
<A= 470
<O= 1330
180
Supplementary angle
17.
<G= 1050
<H= 950
210
Neither

44. Practice 4.4
Determine if each pair of angles is
complentary, supplementary or neither.
18.
<V= 180
<Y= 720
Complementary angle
19.
<B= 980
<L= 820
Supplementary

45. Practice 4.4
20. <1=1650
<2= 150
21. <1=560
<2=1240
22. <1=1480
<2=320

46. Practice 4.4
23. <1=940
<2= 860
<3=94 0
860
Find the measure for all angles.
24. <1=730
<2= 1070
<3=73 0
1070
25. <1=139 0
<2=41 0
<3=139 0
41 0

47. Practice 4.4
26. 450
Measure each angle tomthe nearest degre using a protractor. Write the numbers
of degrees in the angle
27. 300
28. 1200
31. 1500
29. 800
30. 650
34. 1250
33. 600
32. 900

48. Practice 4.4
35. <ABC=450
<BCA= 450
<CAB=90 0
Measure the angles in this geometry shapes.
36. <ABC=1020
<BCD= 780
<CDA=1020
<DAB=78 0

49. Measuring Angles
460

50. What is the measure of the angle?
155°

51. What is the measure of the angle?
18°

52. What is the measure of the angle?
37°

53. What is the measure of the angle?
155°

54. What is the measure of the angle?
95°

55. What is the measure of the angle?
114°

56. What is the measure of the angle?
75°

57. COOMPLETE EXERCISES FROM 43
TO 51