1. Section 1-4
Pairs of Angles

2. Adjacent Angles Definition:
A pair of angles with a shared vertex and common side but do not have overlapping interiors.
Example 1:
1 and 2 are adjacent. 3 and 4 are not.
1 and ADC are not adjacent. 4 3
Adjacent Angles( a common side )
Non-Adjacent Angles

3. Linear Pair
A Linear Pair is a pair of adjacent angles whose non common sides are opposite rays, which form a 180 degree angle.

4. Example 1 Tell whether the pair of angles are adjacent, adjacent and form a linear pair, not adjacent, or form a linear pair
and
Adjacent AND Linear Pair
and
Not Adjacent
and
Adjacent

5. Complementary Angles Definition: Examples: Adjacent Angles
A pair of angles whose sum is 90˚.
**The angles DO NOT have to be adjacent!!**
Examples:
Adjacent Angles
( a common side )
Non-Adjacent Angles

6. Complementary 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

7. Supplementary Angles Definition: A pair of angles whose sum is 180˚
Examples:
Adjacent supplementary angles are also called “Linear Pair.”
Non-Adjacent Angles

8. 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

9. Vertical Angles Definition of Two angles are vertical iff they are two
nonadjacent angles formed by a pair of
intersecting lines.
Vertical angles are ALWAYS CONGRUENT!!
Vertical angles:
1 and 3 1 4 2
2 and 4 3

10. “Think and Discuss” (Grey Box)
Assignment #8
Pg. 31
“Think and Discuss” (Grey Box)
#1-3

11. Example 1
Name each pair of vertical angles.

12. Example 2 Find the measure of the following:
A complement of this angle:
A supplement of this angle:

13. Example 3 Find the measure of the following:
A complement of this angle:
A supplement of this angle:

14. Example 4
An angle measures three degrees less than twice the measure of its complement. Find the measure of it’s complement.

15. Example 5
An angle measures 12 degrees more than ½ the measure of it’s supplement. Find the measure of the angle.