Adjacent Supplementary Angles

Introduction of supplementary angle:

1) If the sum of the measures of two angles is 180, the angles are auxiliary.

2) In other words, if the outer rays of two adjacent angle form a straight angle then the sum of their measures is 180

Note: to remember which word goes with which total, remember that they are in both alphabetical and numerical order: Complementary comes before Supplementary angle alphabetically, and 90 comes before 180 numerically.

Adjacent Angle:

Adjacent angles are pairs of angles that have the same vertex, share one side, but do not have any interior points in common.

More about Adjacent Angle:
Two angles with a common vertex and a common side, but no common interior points, are called adjacent angles.

In the above figure, `angle`DAC and `angle`BAC are adjacent angles; `angle`DAB and `angle`BAC are not adjacent angles.

If the two non-common sides of adjacent angles form opposite rays, then the angles are called a linear pair. Note that x and y are supplementary.

More about Supplementary Angles:
Two angles are supplementary and each is a supplement of the other if they are respectively congruent to the angles of a linear pair. Similarly, we define three angles to be supplementary if they are respectively congruent to the angles of a linear triple.

It easily follows, using the supplement postulate, that two angles are supplementary if and only if the sum of their measures in 180.

Principles for supplementary angles:

1) If two supplementary angles contain a and b, then a+b=108

Thus if angle of a and b are supplementary and a=140, then b=40

2) Adjacent angles are supplementary if their exterior sides lie in the same straight line.

3) If supplementary angles are congruent, each of them is a right angle (Equal supplementary angles are right angles).