1.5 Complementary and Supplementary Angles

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1. WARM UP 1/22/13
Mark no school on 1/20/13.
Identify the type of angle:
1.30°8. 60 °
2.120 °9. 158 °
3.180 °10. 80 °
4.90 °
5.72 °
6.140 °
7.116 °

2. Complementary Angles
Two angles are called complementary angles if the
sum of their degree measurements equals 90 degrees.
Example:
These two angles are complementary. WHY????

3. These two angles can be "pasted"
together to form a right angle!

4. Supplementary Angles
Two angles are called supplementary angles if the sum
of their degree measurements equals 180 degrees.
Example:
These two angles are supplementary. WHY???

5. These two angles can be "pasted"
together to form a straight line!

6. Vertical Angles
Pairs of Angle formed by the intersection of 2 lines.
They are across from each other.
How many pairs?

Vertical angles
are
congruent!!!

7. Review
State whether the following are acute, right, or obtuse.
1.
2.
3.
4.
5.
?
?
acute
obtuse
right
obtuse
acute

8. Complementary and
Supplementary
1. Two angles are complementary. One measures 65 degrees.
2. Two angles are supplementary. One measures 140 degrees.
Find the missing angle.
Answer : 25
Answer : 40

9. Complementary and
Supplementary
Find the missing angle. You do not have a protractor.
Use the clues in the pictures.
1.
2.
x
55 165
x
X=35
X=15

10. Vertical Angles
Find the missing angle. You do not have a protractor.
Use the clues in the pictures.
58
x
X=58

11. Identify Complements and Supplements
•Determine whether the angles are
complementary, supplementary, or neither.
a.
a. Because 22° + 158° = 180°, the angles are
supplementary.
22°
158°

12. •Determine whether the angles are complementary,
supplementary, or neither.
b.
b. Because 15° + 85° = 100°, the angles are neither
complementary or supplementary.
15°
85°

13. •Determine whether the angles are complementary,
supplementary, or neither.
c.
c. Because 55° + 35° = 90°, the angles are
complementary.
35°
55°

14. Example Identify Complements and Supplements
Determine whether the angles are complementary,
supplementary, or neither.
a. b. c.
SOLUTION
a.Because 22° + 158° = 180°, the angles are
supplementary.
b.Because 15° + 85° = 100°, the angles are neither
complementary nor supplementary.
c.Because 55° + 35° = 90°, the angles are
complementary.

15. Checkpoint Identify Complements and Supplements
ANSWER supplementary
ANSWER complementary
Determine whether the angles are complementary,
supplementary, or neither.
1.
ANSWER neither
2.
3.

16. •Tell whether the numbered angles are adjacent
or nonadjacent.
a.
a.Because the angles do not share a common
vertex or a common side, then
and are nonadjacent.
1
2
2Ð
1Ð

17. •Tell whether the numbered angles are
adjacent or nonadjacent.
b.
Because the angles share a common vertex
and a common side, and they do not have
an common interior points, and
are adjacent.
3
4
4Ð3Ð

18. • Tell whether the numbered angles are adjacent or
nonadjacent.
c.
Although and share a common
vertex, they do not share a common side. Therefore,
and
are nonadjacent.
5
6
6Ð5Ð
5Ð 6Ð

19. Example Measures of Complements and Supplements
ÐA is a complement of ÐC, and mÐA = 47°. Find mÐC.a.
b.ÐP is a supplement of ÐR, and mÐR = 36°. Find mÐP.
SOLUTION
a.ÐA and ÐC are
complements, so their
sum is 90°.
b.ÐP and ÐR are supplements,
so their sum is 180°.
mÐA + mÐC = 90° mÐP + mÐR = 180°
47° + mÐC = 90° mÐP + 36° = 180°
47°+ mÐC – 47° = 90° – 47°mÐP + 36° – 36° = 180° – 36°
mÐC = 43° mÐP = 144°

20. Checkpoint Measures of Complements and Supplements
ÐB is a complement of ÐD, and mÐD = 79°. Find mÐB.4.
5.ÐG is a supplement of ÐH, and mÐG = 115°. Find mÐH.
ANSWER 11°
ANSWER 65°

21. Congruent Complements Theorem
1 1
2 3

22. Congruent Supplements Theorem
1 1
2
3

23. SOLUTION
Ð7 and Ð9 are both supplementary to Ð8. So, by the
Congruent supplements Theorem, Ð7 @ Ð9.
Ð7 and Ð8 are supplementary, and
Ð8 and Ð9 are supplementary.
Name a pair of congruent angles.
Explain your reasoning.

24. ANSWER
Ð10 @ Ð12; Ð10 and Ð12 are both
complementary to Ð11, so Ð10 @ Ð12 by
the Congruent Complements Theorem.
In the diagram, mÐ10 + mÐ11 = 90°, and
mÐ11 + mÐ12 = 90°.
Name a pair of congruent angles.
Explain your reasoning.

25. More drawings
20
C
J
D
E
F
G
H
70
90
70
20
90
I

26. Final Drawing
52
B
A
F E
D
C
60
G
68
68
60
52