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).
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
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).
