## Angles An angle is formed when two lines intersect at a point called the vertex.

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

### Notation

Two lines intersect at A. The intersection of these two lines form angles.

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. or a ### Measurement

A degree is defined as of one revolution or turn.

i.e. 360° = one revolution

A minute is defined as 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.

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 180° Straight Between 180° and 360° Reflex ### Properties of Angles

 Equal angles are called congruent angles. Adjacent angles on a straight line add up to 180° a + b = 180° Angles around a point add up to 360° c + d + e = 360° Vertically opposite angles are equal. f = g, h = i Interior angles of a triangle add up to 180° k + l + m = 180° Interior angles of a quadrilateral add up to 360° p + q + r + s = 360°

### Parallel Lines

A line crossing two or more other lines is called a transversal.

With a transversal and a pair of parallel lines:

 Corresponding angles are equal p = t, q = u, r = v, s = w   Alternate angles are equal. r = u, s = t Co-interior angles add up to 180° r + t = 180os + u = 180° Parallel lines