Pairs of Angles (Opposite, Adjacent and Supplementary)

If you need to first, you can read about acute, right and obtuse angles here.

In this entry, you will learn about opposite angles, adjacent angles, corresponding angles, complementary angles and supplementary angles.

Opposite Angles

When two lines intersect, four angles are created. One set of two of these angles are equal to each other, and the other set of two are as well—making two pairs of equal angles. Each pair of equal angles are called opposite angles. In the figure below, the angles denoted by the two blue arcs are opposite angles to one another, as are the angles denoted by the red arcs.

Adjacent Angles

When two angles have the same vertex and one side in common, we call them adjacent angles, like this:

Corresponding Angles

A line crossing two parallel lines makes two intersections and eight angles. For each angle in each intersection, there is an identical angle in the other intersection—one that is the exact same size. These pairs of angles are called corresponding angles.

Complementary Angles

When two angles together add up to $90$${}^{\circ }$, like this, they’re called complementary angles:

Supplementary Angles

When two angles together add up to $180$${}^{\circ }$, like these two, they’re called supplementary angles: