1. Complementary and Supplementary angles

2. Adjacent Angles When you “split” an angle, you create two angles.
The two angles are called
_____________ A C B
adjacent angles D
adjacent = next to, joining. 2 1
1 and 2 are examples of adjacent angles. They share a common ray.
Name the ray that 1 and 2 have in common. ____

3. Adjacent Angles Adjacent angles are angles that:
Definition of
Adjacent
Angles
Adjacent angles are angles that:
A) share a common side
B) have the same vertex, and
C) have no interior points in common M J N R 1 2
1 and 2 are adjacent
with the same vertex R and
common side

4. Adjacent Angles and Linear Pairs of Angles
Determine whether 1 and 2 are adjacent angles.
No. 1 2
Yes. 1 2 X D Z
In this example, the noncommon sides of the adjacent angles form a
___________.
straight line
linear pair
These angles are called a _________

5. Linear Pairs of Angles Note:
Definition of
Linear Pairs
Two angles form a linear pair if and only if (iff):
A) they are adjacent and
B) their noncommon sides are opposite rays C A D B 1 2
1 and 2 are a linear pair.
Note:

6. Complementary and Supplementary Angles
Definition of
Complementary
Angles
Two angles are complementary if and only if (iff)
The sum of their degree measure is 90.
60° D E F
30° A B C
mABC + mDEF = = 90

7. Complementary and Supplementary Angles
If two angles are complementary, each angle is a complement of the other.
ABC is the complement of DEF and DEF is the complement of ABC.
60° D E F
30° A B C
Complementary angles DO NOT need to have a common side or even the same vertex.

8. Complementary and Supplementary Angles
Some examples of complementary angles are shown below.
75° I
mH + mI = 90
15° H
50° H
40° Q P S
mPHQ + mQHS = 90
30°
60° T U V W Z
mTZU + mVZW = 90

9. Complementary and Supplementary Angles
If the sum of the measure of two angles is 180, they form a special pair of angles called supplementary angles.
Definition of
Supplementary
Angles
Two angles are supplementary if and only if (iff) the sum of their degree measure is 180.
130° D E F
50° A B C
mABC + mDEF = = 180

10. Complementary and Supplementary Angles
Some examples of supplementary angles are shown below.
105° H
75° I
mH + mI = 180
50° H
130° Q P S
mPHQ + mQHS = 180
60°
120° T U V W Z
mTZU + mUZV = 180
and
mTZU + mVZW = 180