1. 1.5 Describe Angle Pair Relationships
Objective: use special angle relationships to find angle measures
Construction activity

2. Relationships based on Measurements
Complementary
Supplementary
Adjacent

3. Complementary Angles
Two angles that have a sum of 90 degrees. They may or may not be right next to each other.

4. Supplementary Angles
Two angles that have a sum of 180 degrees. They may or may not be right next to each other.

5. Complementary or Supplementary?

6. Tricks to Keep From Mixing Them Up
C comes first in the alphabet and 90 is smaller that 180
C for corner (90 degrees), S for straight (180 degrees)
Others?

7. Adjacent 2 angles next to each other
Must share a common side and vertex

8. EXAMPLE 1
Identify complements and supplements
In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles.
SOLUTION
Because 32°+ 58° = 90°, BAC and RST are complementary angles.
Because 122° + 58° = 180°, CAD and RST are supplementary angles.
Because BAC and CAD share a common vertex and side, they are adjacent.

9. Guided Practice 1 – 2 pg.35

10. GUIDED PRACTICE
for Example 1
In the figure, name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles. 1.
FGK and GKL,
HGK and GKL,
FGK and HGK
ANSWER

11. GUIDED PRACTICE
for Example 1
Are KGH and LKG adjacent angles ? Are FGK and FGH adjacent angles? Explain. 2.
No, they do not share a common vertex.
No, they have common interior points.
ANSWER

12. EXAMPLE 2
Find measures of a complement and a supplement
Given that 1 is a complement of and m = 68°,
find m
SOLUTION
a. You can draw a diagram with complementary adjacent angles to illustrate the relationship.
m = 90° – m = 90° – 68° = 22°

13. EXAMPLE 2
Find measures of a complement and a supplement
b. Given that is a supplement of 4 and m = 56°,
find m 3.
SOLUTION
b. You can draw a diagram with supplementary adjacent angles to illustrate the relationship.
m 3 = 180° – m 4 = 180° –56° = 124°

14. EXAMPLE 3
Find angle measures
Sports
When viewed from the side, the frame of a ball-return net forms a pair of supplementary angles with the ground. Find m BCE and m ECD.

15. Extra Example 3
Two roads intersect to form supplementary angels, angle XYW and angle WYZ. Find the measure of angle XYW and angle WYZ.

16. Guided Practice 3 - 5

17. GUIDED PRACTICE
for Examples 2 and 3
3. Given that is a complement of and m = 8o, find m 1.
82o
ANSWER
4. Given that is a supplement of and m = 117o, find m
63o
ANSWER
LMN and PQR are complementary angles. Find the measures of the angles if m LMN = (4x – 2)o and m PQR = (9x + 1)o.
ANSWER
26o, 64o

18. Angle Pairs
Linear Pair
Vertical Angles

19. Linear Pair Adjacent angles that form a straight line
Their noncommon sides form opposite rays.

20. Questions True or False…
Every linear pair of angles is supplementary.
Every pair of supplementary angles is a linear pair.

21. Vertical Angles
Sides form opposite rays

22. EXAMPLE 4
Identify angle pairs
Identify all of the linear pairs and all of the vertical angles in the figure at the right.
SOLUTION
To find vertical angles, look or angles formed by intersecting lines.
1 and are vertical angles.
ANSWER
To find linear pairs, look for adjacent angles whose noncommon sides are opposite rays.
1 and 4 are a linear pair and are also a linear pair.
ANSWER

23. EXAMPLE 5
Find angle measures in a linear pair
Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle.
ALGEBRA
SOLUTION
Let x° be the measure of one angle. The measure of the other angle is 5x°. Then use the fact that the angles of a linear pair are supplementary to write an equation.

24. Find angle measures in a linear pair
EXAMPLE 5
Find angle measures in a linear pair
xo + 5xo = 180o
Write an equation.
6x = 180
Combine like terms.
x = 30o
Divide each side by 6.
The measures of the angles are 30o and 5(30)o = 150o.
ANSWER

25. GUIDED PRACTICE
For Examples 4 and 5
Do any of the numbered angles in the diagram below form a linear pair? Which angles are vertical angles? Explain. 6.
ANSWER
No, no adjacent angles have their noncommon sides as opposite rays, and , and 5, and 6, these pairs of angles have sides that from two pairs of opposite rays.

26. GUIDED PRACTICE
For Examples 4 and 5
7. The measure of an angle is twice the measure of its complement. Find the measure of each angle.
ANSWER
60°, 30°

27. Review Describe each with a short sentence or sketch.
Complementary Angles
Supplementary Angles
Adjacent Angles
Linear Pair
Vertical Angles

28. Homework
1, evens, 17 – 28, 31-38, 49 – 53
Quiz coming up over (study bottom of page 41)