Name of Lecturer: Mr. J.Agius
Course: FCES
LESSON 33
Angles and Shapes
33.1 Angles
In order to measure angles between two lines we usually use a protractor. This is picture
representing a protractor.
Measuring
Protractors usually have two sets of
numbers going in opposite directions. Be
careful which one you use
Have a Go Yourself!
Try to measure the angles A, B, C and D inside this shape.
Be careful which angle you read from the protractor.
Hint: if you get them all correct, they will add up to 360°
Ans: A = _________ B = _________ C = _________ D =_________ Total =_________
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 1
Name of Lecturer: Mr. J.Agius
Course: FCES
53.2 Degrees (Angles)
We can measure Angles in Degrees.
There are 360 degrees in one Full Rotation (one complete circle around).
(Note: "Degrees" can also mean Temperature, but here we are talking about Angles)
The Degree Symbol: °
We use a little circle ° following the number to mean degrees.
For example 90° means 90 degrees
One Degree
This is how large 1 Degree is
The Full Circle
A Full Circle is 360°
It is also called as 1 revolution
Half a circle is 180°
(called a Straight Angle)
Quarter of a circle is 90°
(called a Right Angle)
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 2
Name of Lecturer: Mr. J.Agius
Course: FCES
53.3 Angles On One Side of A Straight Line
Angles on one side of a staight line will always add to 180 degrees. If a line
is split into 2 and you know one angle you can always find the other one.
Example: If we know one angle is 45° what is angle "a" ?
Angle a will be 180° − 45° = 135°
This method can be used for several angles on one side of a straight line.
Example: What is angle "b" ?
In this diagram angle b is simply
180° take away the sum of the
other angles.
Sum of known angles =
45° + 39° + 24° = 108°
Angle b = 180° − 108°
Angle b = 72°
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 3
Name of Lecturer: Mr. J.Agius
Course: FCES
53.4 Names of Angles
As the Angle Increases, the Name Changes
Type of angle
Description
Acute Angle
Right Angle
Obtuse Angle
an angle that
an angle that
an angle that
than 180°
an angle that
an angle that
Straight Angle
Reflex Angle
is less than 90°
is 90° exactly
is greater than 90° but less
is 180° exactly
is greater than 180°
Be Careful What You Measure
This is an Obtuse Angle.
And this is a Reflex Angle.
But the lines are the same ... so when naming the angles make sure
that you know which angle is being asked for!
Parts of an Angle
The corner point of an angle is called the vertex
And the two straight sides are called arms
The angle is the amount of turn between each arm.
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 4
Name of Lecturer: Mr. J.Agius
Course: FCES
Labelling Angles
There are two main ways to label angles:
1. by giving the angle a name, usually a lower-case letter
like a or b, or sometimes a Greek letter like α (alpha) or
θ (theta)
2. or by the three letters on the shape that define the
angle, with the middle letter being where the angle
actually is (its vertex).
Example angle "a" is "BAC", and angle "θ" is "BCD"
Exercise 33A
1.
2.
3.
How many degrees are there
a)
in half a revolution
Ans.______________
b)
in three-quarters of a turn
Ans.______________
c)
in two complete revolutions
Ans.______________
d)
in two-thirds of a turn?
Ans.______________
What angle, in degrees, corresponds to
1
a)
/3 of a right angle
Ans.______________
b)
2 right angles
Ans.______________
c)
0.4 of a right angle
Ans.______________
d)
1.7 of a right angle?
Ans.______________
How many degrees does the hand of a clock turn through when
a)
it starts at 2 and stops at 3
Ans.______________
b)
Ans.______________
it starts at 2 and stops at 11?
In each case state whether the angle is acute, obtuse or reflex.
Ans. a)______________
Ans. b)______________
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 5
Name of Lecturer: Mr. J.Agius
4.
Course: FCES
For each angle in this question
a)
state whether it is acute, obtuse or reflex
b)
estimate its size of angle a by using the protractor
c)
Find the size of angle b by using the rule ANGLES ABOUT A POINT.
(i)
(ii)
a
b
a
b
a
b
(iii)
(iv)
a
b
Answers
Acute/ Obtuse
i
Size of Angle
a
b
ii
a
b
iii
a
b
iv
a
b
5.
Work out the lettered angles, giving reasons in each case.
a)
b)
d
135o
62o
x
o
74
Ans. d = ___________
Ans. x = ___________
Reason:___________________________
Reason:_______________________
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 6
Name of Lecturer: Mr. J.Agius
c)
Course: FCES
d)
f
120
o
o
100
m
f
Ans. m = ___________
Ans. f = ___________
Reason ___________________________
Reason ___________________________
e)
f)
a
b
48o
o
55o 45
x
Ans. a = ___________
Ans. x = ___________
Reason ___________________________
Reason ___________________________
Ans. b = ___________
h)
Reason ___________________________
p
35o
q
g)
Ans. p = ___________
y
32o
Reason ___________________________
Ans. y = ___________
Ans. q = ___________
Reason ___________________________
Reason ___________________________
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 7
Name of Lecturer: Mr. J.Agius
Course: FCES
Mixed Exercise
1) Measure these angles as accurately as you can
a)
b)
2) Work out the number of degrees in
a) 2 revolutions
b)
1 ½ revolutions
c) 1.2 revolutions
90o
c) 270o
3) What fraction of a complete turn is
a) 180o
b)
4) Label each of these angles as acute, obtuse or reflex.
a)
b)
c)
d)
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 8
Name of Lecturer: Mr. J.Agius
Course: FCES
5) Find the angles marked with letters in these diagrams. Give reasons for your answers.
o
162
47o
94o
71o
58o
90o
83o
co
bo
ao
48o
60o
42o
o
e
61o
86o
o
o
47
do
57o
71
fo
ho
i
go
o
44o
ko
ko
jo
j
o
j
o
ko
ko
ko
no
lo
50o
lo
po
112o
mo
Learning Outcome 5 – Classify, draw and work with various shapes and objects
Page 9