Notation
An angle is formed when two lines or rays meet at the same point. The meeting point is called thevertex of the angle.
The angle formed is written as  BAC or BÂC.
The vertex of the angle is always represented by the middle letter.
A single letter can also be used to represent an angle e.g. Â or a
Measurement of Angles
A degree is defined as  of one revolution or turn.
i.e. 360° = one revolution
Angles can be measured using a protractor (see Topic 29).
Types of Angles
- Complementary angles add up to 90o.
- Supplementary angles add up to 180o.
- Congruent angles are equal.
- Adjacent angles are next to one another and have a common vertex and line.
p and q are adjacent angles.
Angles that lie within a certain range of values are given special names.
| Angle size |
Name |
Examples
|
|
Between 0° and 90°
|
Acute |
 |
|
90°
|
Right
|
 |
|
Between 90° and 180°
|
Obtuse
|
 |
|
180o
|
Straight
|
 |
|
Between 180° and 360°
|
Reflex
|
 |
Properties of Angles
Adjacent angles on a straight line
|
Property
|
Diagram
|
|
Adjacent angles on a straight line add up to 180°.
( Adj. s on st. line add up to 180°)
|
 a + b = 180° |
|
Example
|
|
Find the value of a
|
a + 69 + 41 = 180
( Adj. s on st. line add up to 180°)
a + 110 = 180
a = 180 − 110
a = 70o
|
Angles around a point
|
Property
|
Diagram
|
|
Angles around a point add up to 360°
(s at a pt. add to 360°) |
 c + d + e = 360° |
|
Example
|
|
|
z + 65 + 154 = 360
(s at a pt. add to 360°)
z + 219 = 360
z = 360 − 219
z = 141o
|
Vertically opposite angles
|
Property
|
Diagram
|
|
Vertically oppostite angles are equal or congruent.
(Vert. opp. s equal) |
f = g and h = i
|
|
Example
|
|
|
y = 119o (Vert. opp. s equal) |
|
