## Angles ### 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 = 180a = 180 − 110a = 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 = 360z = 360 − 219z = 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)