Angles and Lines

Lines.jpgAn angle is formed when two lines intersect at a point called the vertex.

Angles are usually measured in degrees ( o ) and minutes ( ' ), although there are other systems of measuring angles, such as radians.

 

Notation
Measurement
Types of Angles
Properties of Angles

 

Notation

Two lines intersect at A. The intersection of these two lines form angles.
The angle formed is written as ∠'BAC or BY9_Angles_and_Lines_02.gifC.
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

 Y9_Angles_and_Lines_01.gif

Measurement of Angles

A degree is defined as 1⁄360th of one revolution or turn. i.e. 360° = one revolution

A minute is defined as 1⁄60th of a degree. i.e. 1 degree = 60 minutes (1° = 60')

 

Types of Angles

  • Complementary angles add up to 90°
  • Supplementary angles add up to 180°
  • Adjacent angles are next to one another and have a common vertex and line.
  • Equal angles are called congruent angles.

p and q are adjacent angles.Y9_Angles_and_Lines_05.gif

Angles that lie within a certain range of values are given special names

 

Angle size
Name
Examples

Between 0° and 90°
Acute
Y9_Angles_and_Lines_06.gif

90°
Right
Y9_Angles_and_Lines_07.gif

Between 90° and 180°
Obtuse
Y9_Angles_and_Lines_08.gif

180°
Straight
Y9_Angles_and_Lines_09.gif

Between 180° and 360°
Reflex
Y9_Angles_and_Lines_10.gif

 

Properties of Angles

 

Adjacent angles on a straight line add up to 180° 

(Adj. ∠'s on st. line are supp.)
Y9_Angles_and_Lines_11.gifa + b = 180°
 Example

Angles around a point add up to 360° 

(∠'s at a pt. add to 360°)
Y9_Angles_and_Lines_12.gifc + d + e = 360°
 Example

Vertically opposite angles are equal.

(Vert. opp. ∠'s equal.)
Y9_Angles_and_Lines_13.giff = g, h = i

 

 Example