MATHEMATICS - FORM 1
LINES AND ANGLES
ANGLES
A) Identifying an Angle
Angle is formed by two straight lines that meet
at a point called the vertex.
For example : -
In the figure above,
(a) AOB is an angle.
(b) OA and OB are called the arms of the angle.
(c) O is the vertex, that is the point where the two
arms meet.
B) Naming an angle
An angle can be named by using one letter
or three letters.
For example :-
C) Measuring Angles
1. Angles are measured in units called degrees
( 0 ).
2. To measure an angle, we can use an instru-
ment called the protractor as shown below.
3. Note that if we read from left to right ( clockwise
direction ), we use the inner scale.
4. To measure an angle less than 1800, <KLM, follow
the steps below.
Method 1 :
Step 1
Place the protractor that its centre is on the vertex.
L. Adjust the protractor until its base line corresponds
with the arm LM.
Step 2
Read the value of <KLM using the inner scale.
Therefore, <KLM = 300.
Method 2 :
Step 1
Place the protractor so that its centre is on the
vertex L. Adjust the protractor until its base line
corresponds with the arm LK.
Step 2
Read the value of <KLM using the outer scale.
Therefore, .KLM = 300
5. To measure an angle which is more than 1800,
follow the steps below :
To measure <STU
Step 1
Produce the arm ST to V and measure <STV.
<STV = 1800
Step 2
Place and adjust the protractor as shown to
measure <VTU.
Step 3
<STU = <STV + <VTU
= 1800 + 200
= 2000
D) Identifying the Different Types of Angles
The table below shows the different types of angles.
E) Determining the Sum of Angles on a
Straight Line
1. Use a protractor to measure the angles on the
straight line.
Worked Example 4
Using a protractor, measure the angles on the
straight line KLM. Then, find the sum of the
angles in each case.
(a) (b)
Solution
(a) x = 1200 , y = 600
x + y = 1200 + 600
= 1800
(b) p = 400 , q = 900 , r = 500
p + q + r = 400 + 900 + 500
= 180
2. In general, the sum of the angles on a straight
line is 1800.
For example :-
AOB is a straight line.
x + y + z = 1800
E) Determining the Sum of Angles in
One Whole Turn
1. A protractor is used to measure the angles
at a point.
Worked Example 5
Use a protractor to measure the angles in the
figures. Then, find the sum of the angles in each
case.
(a) (b)
Solution
(a) x = 1100 , y = 2500
x + y = 1100 + 2500
= 3600
(b) p = 1300 , q = 600 , r = 700 , s = 1000
p + q + r + s = 1300 + 600 + 700 + 1000
= 3600
2. In general, the sum of the angles that formed
one whole turn is 3600.
For example :-
a + b + c + d + e = 360
PARALLEL LINES AND
PERPENDICULAR LINES
A) Determining Parallel Lines
1. Parallel lines are lines that will not meet
however far they are produced either way.
2. They are at the same distance apart from
one other
For example :-
(a)
KL is parallel to RS or KL//RS
(b)
AB//CD
(c)
EF//HG
EH//FG
B) Determining Perpendicular Lines
1. If two straight lines intersect at 90 , we say the two
lines are perpendicular to each other.
For example :-
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