What is the smallest angle that can be drawn? The figure below shows two lines (CACA and ABAB) making an angle at a common vertex AA. If line CACA is rotated around the common vertex AA, down towards line ABAB, then the smallest angle that can be drawn occurs when the two lines are pointing in the same direction. This gives an angle of 0∘∘. This is shown in Figure 6

If line CACA is now swung upwards, any other angle can be obtained. If line CACA and line ABAB point in opposite directions (the third case in Figure 6) then this forms an angle of 180∘∘.

If three points AA, BB and CC lie on a straight line, then the angle between them is 180∘∘. Conversely, if the angle between three points is 180∘∘, then the points lie on a straight line.

An angle of 90∘∘ is called a *right angle*. A right angle is half the size of the angle made by a straight line (180∘∘). We say CACA is *perpendicular* to ABAB or CA⊥ABCA⊥AB

. An angle twice the size of a straight line is 360

∘∘. An angle measuring 360

∘∘ looks identical to an angle of 0

∘∘, except for the labelling. We call this a

*revolution*.

All angles larger than 360∘∘ also look like we have seen them before. If you are given an angle that is larger than 360∘∘, continue subtracting 360∘∘ from the angle, until you get an answer that is between 0∘∘and 360∘∘. Angles that measure more than 360∘∘ are largely for mathematical convenience.

*Acute angle*: An angle ≥0∘≥0∘ and <90∘<90∘.
*Right angle*: An angle measuring 90∘90∘.
*Obtuse angle*: An angle >90∘>90∘ and <180∘<180∘.
*Straight angle*: An angle measuring 180∘∘.
*Reflex angle*: An angle >180∘>180∘ and <360∘<360∘.
*Revolution*: An angle measuring 360∘360∘.

These are simply labels for angles in particular ranges, shown in Figure 8.

Once angles can be measured, they can then be compared. For example, all right angles are 90∘∘, therefore all right angles are equal and an obtuse angle will always be larger than an acute angle.

The following video summarizes what you have learnt so far about angles.

Note that for high school trigonometry you will be using degrees, not radians as stated in the video. Radians are simply another way to measure angles. At university level you will learn about radians.

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