Introduction to Angles
We begin our study of
angles by learning what they are, how to name them, and ways in which angles
can be classified. These concepts are explained below.
An angle is formed when two rays meet at a common endpoint, or vertex. The two sides
of the angle are the rays, and the point that unites them is called the vertex.
The vertices are shown in red in the diagram above
Angles can be named in various ways. One way is to use the ? symbol accompanied
by three letters. The first and third letters indicate points on the two rays. The
letter in the middle is the vertex. Note that the first and third letters are interchangeable
because they both measure the same angle. Another way to label an angle is by just
using the ? symbol accompanied by the vertex point alone. However, this method only
works when there is only one angle at the vertex point. If more than one angle is
formed at a vertex point, we need to specify which angle we are talking about by
naming it in a different way. Finally, the last way to label an angle is by using
the ? symbol accompanied by the letter or number shown between the angle. The different
ways of labeling an angle are shown below.
The angle above can be called ?ABC, ?CBA, ?B, or ??
Classifications of Angles
Angles can be measured in degrees or radians. For the time being, we will strictly
talk about angles in terms of their degree measure. The symbol for degrees is °.
Angles can measure from 0° up to 360°. Angles with no measure are called zero angles,
while angles of 360° are full rotations. For our study of geometry, we will primarily focus on three important
classifications of angles: acute, obtuse, and right.
A right angle is an angle whose measure is exactly 90°. An easy way to determine
whether an angle is a right angle is by considering whether a small square could
fit perfectly in the corner of the intersection of the two lines that form the angle.
While you would need a protractor to give a more precise measurement, this can give
you an approximation of whether or not an angle is close to 90°.
An acute angle is an angle whose measure is less than 90°. For these kinds of angles,
a square could not fit perfectly at the intersection of the two lines that form
Obtuse angles have measures greater than 90° but less than 180°.
If an angle’s measure is 180°, it is called a straight angle. Straight angles are
just lines with three points on them.