Measuring angles
An angle’s arms can be drawn as long or as short as you like. So what exactly is being measured, and how do you put a number on it?
Where you are 5 inside
What this area is about
The size of an angle is not the length of its arms. It is how far one arm has to turn to land on the other. This area turns that idea into a number, the degree, and gives you a tool for reading and drawing it.
How these fit together
The idea and the unit. An angle is an amount of turn says what the size of an angle is. Degrees count that turn: a full turn is 360^\circ and a right angle is 90^\circ.
The tool. Measuring and drawing angles with a protractor reads the degrees off a drawn angle, or draws an angle of a given size.
A result to use. Angle measures add: when an angle is split into parts, its measure is the sum of the parts, so a missing part is the whole minus the rest.
An application. Bearings and navigation uses angles as directions of travel. It also needs sine, cosine and the Pythagorean theorem, so it is high school work.
A path through it
Turn first, then degrees, which builds on it. Then the protractor, then angles adding. Leave bearings until you have met right triangle trigonometry.
Finish here and you can name and compare angles by size, sort them into acute, right and obtuse, and move on to angle pairs and circle graphs.