Angles - Automaths

Lines and angles A line is an infinite number of points between two end points Where two lines meet or cross they form an angle An angle is an amount of rotation It is measured in degrees Types of angles Name of angle Example

Warm Up: Use the diagram below to list all the pairs of vertical angles Use the angle numbers (1-8) to list of the vertical angles If the measure of

s(the ray itself) – which we call a trivial physical angle and the entire plane – which we call a complete physical angle So unless we are dealing with a straight physical angle the two physical angles enclosed by \\s 1s 2 are clearly distinguishable: one is “small” (the inner angle); the other is “big” (the outer angle)

further to make a bigger angle then vary the amount of rotation to emphasise the point Are students sure what it » means for something to rotate? The key thing here is that » the angle is the rotation of one ray about another ray through a common point The angle changes as we change the amount of rotation The two rays which make »

Angles in a straight line total 180° 2 x + 30 ° + x = 180 ° \\ 3 x = 180 ° - 30 ° = 150 ° x = 50 ° If the sum of two angles is 180o then they are called supplementary angles Either one is called the supplement of the other is the complement of and vice versa ° + b ° = 90 °

In a rectangular coordinate system angles are defined as the called the initial side and the ray at then ending position is the terminal side Rotation in a counterclockwise direction is positive and rotation in a clockwise direction is negative