Download Types of Angles

Types of Angles
Picture
Name of Angle
Description
Acute Angle
I am the smallest type of
angle and I am very CUTE. I
am always less than 90º.
Right Angle
I am perfectly straight and
always RIGHT. I am exactly
90º.
Obtuse Angle
I am a lot more relaxed than
the Right Angle, and therefore
OBviously more than 90º,
but less than 180º.
Straight Angle
I like to walk on the
STRAIGHT and narrow line, I
never go anywhere but 180º.
Reflex Angle
I am so FLEXible that I can
bend all the way past 180º.
Revolution/Full Angle
I don’t like to be like the rest,
I want a REVOLUTION and
we can all dance in a circle. I
am exactly 360º.
Charlie says: “Always
start on the horizontal
line, then walk towards
the angled line.”
45º
129º
180º
135º
360º
2
Measuring and Drawing Angles
When measuring angles, we use a protractor. A protractor has an inner scale
and an outer scale. The way in which the angle faces, will indicate to you if
you should use the inner or outer scale to measure or draw the angle.
Acute angle, facing left, will
be measured or drawn using
the outer scale (0º— 90º)
Acute angle, facing right, will
be measured or drawn using
the inner scale (0º— 90º)
Obtuse angles,
facing right, will
be measured with
the inner scale
(90º—180º)
Obtuse angles,
facing left, will be
measured with the
outer scale
(90º—180º)
A
STEPS to follow when measuring angles:
Step 1: Make sure which angle you should be measuring.
ABC, means you have to measure angle B.
Step 2: Extent any lines with your ruler to ensure
that you can see the line all the way past your
protractor.
Step 3: Make a dot where the two lines meet, big
enough for you to see through the protractor. This
will help you put the protractor exactly in the
middle.
Step 4: Decide if you will measure with the inner
or outer scale, using the explanation above.
B
C
Step 5: Make sure your protractor is exactly straight on the bottom line and that your dot
is exactly on the perpendicular line facing towards 90º.
Step 6: Measure the angle—in this example, the angle measures 55º.
STEPS to follow for drawing perfect angles:
Step 1: Always start with a dot where you would like to draw your angle, then draw a
straight horizontal line from where you will begin.
Step 2: Measure the angle using your protractor. Remember to follow the instructions
carefully. Is it facing right or left? Will it be an Acute angle or an Obtuse angle? The
answer to these questions will tell you if you will be using the inner or outer scale.
Step 3: Make a visible mark at exactly the correct degrees. Remember to make sure that
your protractor does not move while you are measuring.
Step 4: Connect your dot with that mark, using a ruler.
Step 5: Draw a semi-circle or a square (90º) to indicate the angle you have measured
and write in the degrees of that angle.
2
3
Measuring and Drawing Angles
STEPS to follow when measuring Reflex Angles:
A
Step 1: Make sure which angle you should be measuring.
B
ABC, means you have to measure angle B.
Step 2: Extent one line to form a straight line, in
this example it will be line AB. The angle of the extended
line is equal to 180º (red arrow).
Step 3: Flip your protractor and now measure the angle
from the extended line to line BC.
Remember to check if you should be using the inner or
outer scale of the protractor.
Step 4: In this example the angle measures 45º.
Step 5: Now add this answer to the 180º of the straight
angle. Your answer will be 180º + 45º = 225º
C
A
B
C
A
B
C
Fast Facts
Angles:
An angle is formed by two rays with the same starting point.
The starting point is called the vertex.
Remember that the sum of
The two rays are also called the sides of the angle.
all the angles of a triangle is
Angles are measured using a protractor.
180º.
Triangles:
Triangles are classified with reference to their angles and their rays/
sides.
Looking only at the angles of a triangle, it can be classified as;

acute angled—all angles less than 90º,

right angled—one angle exactly 90º, or

obtuse angled—at least one angle more than 90º.
Looking only at the rays or sides of the triangle, it can be classified as;

an equilateral triangle—all 3 sides/rays are congruent or the same
length (all 3 angles will also be equal),

an isosceles triangle—2 sides/rays are congruent or the same length
(2 angles will be equal), or

a scalene triangle—no sides/rays are congruent or the same length
(no angles will be equal).
When classifying a triangle, we first classify it according to its angles and then
according to its rays or sides, e.g.
Right-angled, isosceles triangle
Acute, equilateral triangle
Obtuse, scalene triangle
3
4
Measuring and Drawing Angles
Measure the following angles, using your protractor:
TIP: Turn the page, until one of the sides of the angle is horizontal.
C
X
Y
D
E
Z
Type of angle:
Type of angle:
Size of
Size of
CDE:
XYZ:
R
F
E
S
G
T
Type of angle:
Type of angle:
Size of
Size of
EFG:
RST:
17
H
K
93
70
I
L
M
G
Type of angle:
Type of angle:
Size of
Size of
GHI:
4
KLM:
5
Drawing Angles and Triangles
Draw the following angles in the space provided:
ABC, ABC, 195º, left facing
Right angled, isosceles triangle
Acute, equilateral triangle
MNO, 285º, right facing
JKL, 305º, right facing
Obtuse, scalene triangle
5
6
Classifying Triangles
Complete the following tables by classifying the triangles,
first by angles and then by sides:
Use your protractor/ruler if you are not sure.
G
E
B
A
F
H
D
C
Triangle
Classify by angles
Classify by sides
A
B
C
D
E
F
G
H
Calculate angles without measuring:
Determine the value of
2.
D
D
x
39
x
3.
F
F
x
F
14
6
1.
x;
92
84
19
E
D
E
E
x
= ________________
= ________________
x=
________________
= _________________
6
x = ______________
= ______________
7
Measuring and Drawing Angles—Memo
Measure the following angles, using your protractor:
HINT: Turn the page, until the angle you have to measure is horizontal
43.5
C
X
Y
E
49.5
84
D
92.9
43.6
Z46.5
Type of angle: Obtuse
Type of angle: Acute
Size of
Size of
CDE: 92º
15
.8
R
G
XYZ: 84º
E
14
8
S
1T
6.2
F
Type of angle: Reflex
Type of angle: Obtuse
Size of
Size of
EFG: 210º
RST: 148º
17
H
M
70
I
L
93
K
G
Type of angle: Acute
Type of angle: Reflex
Size of
Size of
GHI: 17º
7
KLM: 330º
8
Measuring and Drawing Angles—Memo
Draw the following angles in the space provided:
ABC, ABC, 195º, left facing
Right angled, isosceles triangle
A
45
195
B
A
C
45
B
Acute, equilateral triangle
MNO, 285º, right facing
A
285
M
N
60
B
60
60
C
C
O
JKL, 305º, right facing
Obtuse, scalene triangle
305
J
K
A
135
B
L
8
C
9
Classifying Triangles
Complete the following tables by classifying the triangles
below by angles and by sides:
Use your protractor to measure the angles if you are not sure.
Triangle
Classify by angles
Classify by sides
A
right angled
scalene
B
obtuse
scalene
C
acute
isosceles
D
right
scalene
E
acute
equilateral
F
obtuse
isosceles
G
right angled
isosceles
H
acute
isosceles
Calculate angles without measuring:
Determine the value of
1.
x
x;
2.
= 180º - (39º + 92º)
= 49º
3.
x=
(180º - 84º) ÷ 2
= 48º (isosceles)
9
x = 180º - (146º + 19º)
= 15º