Figure %: Acute and obtuse angles

Interior and Exterior Angles

So far, all of the angles we have looked at and studied have been interior angles. When two rays share a common endpoint, two angles are created. Up until now, we have only studied the interior angle: the angle whose measure is less than 180 degrees. But actually, whenever two rays create an angle of less than 180 degrees, they also create another angle whose measure is 360 degrees minus the measure of the smaller angle. As we said before, the smaller angle, whose measure is less than 180 degrees, is the interior angle. The other angle, which seems to rotate around the "outside" of the interior angle, is the exterior angle. The measure of the exterior angle is always greater than that of the interior angle, and is always equal to 360 degrees minus the measure of the interior angle. Below both are pictured.

Figure %: An Interior and Exterior Angle

Adjacent Angles

In the following sections, we'll study pairs of angles and relationships between angles. In these sections, it will be important to understand properties of angles that lie next to each other. Formally, these angles are called adjacent angles. Three things must be true for angles to be adjacent:

  1. The two angles must share a common vertex.
  2. They must share one common side.
  3. The angles must not share any interior points.
See how each statement is true for the adjacent angles below.
Figure %: Adjacent Angles
Angle CAB is adjacent to angle DAB. The angles share a common vertex, A, a common side, ray AB, and share no interior points (the ray AB is not on the interior of either angle, it only forms a side of each).