Technically speaking, an angle is the union of two rays (lines that extend infinitely in just one direction) that share an endpoint (called the vertex of the angle). The measure of an angle is how far you must rotate one of the rays such that it coincides with the other.
In this guide and for the Math IC, you don’t really need to bother with such a technical definition. Suffice it to say, angles are used to measure rotation. One full revolution around a point creates an angle of 360 degrees, or 360
. A half-revolution, also known as a straight angle, is 180
degrees. A quarter revolution, or right angle, is 90
.
In text, angles can also be indicated by the symbol
.
Vertical Angles
When two lines or line segments intersect, two pairs of congruent (equal) angles are created. The angles in each pair of congruent angles created by the intersection of two lines are called vertical angles:
In this figure,
and
are vertical angles (and therefore congruent), as are
and
.
Supplementary and Complementary Angles
Supplementary angles are two angles that together add up to 180º. Complementary angles are two angles that add up to 90º.
Whenever you have vertical angles, you also have supplementary angles. In the diagram of vertical angles above,
and
,
and
,
and
, and
and
are all pairs of supplementary angles.
Parallel Lines Cut by a Transversal
Lines that will never intersect are called parallel lines, which are given by the symbol ||. The intersection of one line with two parallel lines creates many interesting angle relationships. This situation is often referred to as “parallel lines cut by a transversal,” where the transversal is the nonparallel line. As you can see in the diagram below of parallel lines AB and CD and transversal EF, two parallel lines cut by a transversal will form eight angles.
Among the eight angles formed, three special angle relationships exist:
- Alternate exterior angles are pairs of congruent angles on opposite sides of the transversal, outside of the space between the parallel lines. In the figure above, there are two pairs of alternate exterior angles:
and 
, and 
and 
.
- Alternate interior angles are pairs of congruent angles on opposite sides of the transversal in the region between the parallel lines. In the figure above, there are two pairs of alternate interior angles:
and 
, and 
and 
.
- Corresponding angles are congruent angles on the same side of the transversal. Of two corresponding angles, one will always be between the parallel lines, while the other will be outside the parallel lines. In the figure above, there are four pairs of corresponding angles:
and 
, 
and 
, 
and 
, and 
and 
.
In addition to these special relationships between angles, all adjacent angles formed when two parallel lines are cut by a transversal are supplementary. In the previous figure, for example,
and
are supplementary.
