2.1 Concepts

An angle consists of two rays and one vertex.
You measure the angle in degrees. One rotation around a circle is  360º and is read as “360 degrees”.

This angle is larger than 180º.

There are special cases where the circular arc is replaced by two lines.  This is when the angle is 90º.  A ninety degree angle is also called a right angle.

An angle can be indicated in many different ways.  Here are a few ways write it:
  • Λ x
  • Λ ABC
  • Λ B

In mathematics, the circle's circumference is divided into 360 equal parts. One rotation around the circle is 360 degrees.  It is written 360º.  Instead of writing degrees, we usually use the symbol °.

1 degree = 1°

On an analog clock, there is an hour and minute hand.  In one hour, the minute hand moves one rotation.  The minute hand has moved 360 degrees.

1 rotation = 360.

rotation =
= 180

rotation =
= 90

An angle’s size can also be indicated in the unit radians (rad).  We usually leave off the unit.  In elementary school, we don’t often use radians.  You will learn more about radians in High School.

The relationship between radians and degrees is the following:

1 radian = 360°/2p = 57,3°

1 radian = 360 = 2p rad
(p = Pi)

radian = 180 = p rad

radians = 90 =

A grad is an attempt to adapt angle measurement to the decimal system.

1 grad = 1/100 of a right angle.  One rotation is there for 400 grads and a right angle is 100 grads.

In education, we seldom talk about the grad in mathematics, but it is become more common in the subject geosciences.

1 rotation = 360 = 400 grads

rotation = 180 = 200 grads
rotations = 90 = 100 grads