1. Adjacent, Vertical, Supplementary, and Complementary Angles Linear Pair, Perpendicular Lines

2. Adjacent angles are “side by side” and share a common ray.
15º
45º

3. These are examples of adjacent angles.
45º
80º
35º
55º
130º
50º
85º
20º

4. These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º

5. When 2 lines intersect, they make vertical angles.
75º
105º
105º
75º

6. Vertical angles are opposite from one another.
75º
105º
105º
75º

7. Vertical angles are opposite from one another.
75º
105º
105º
75º

8. Vertical angles are congruent (equal).
150º
30º
150º
30º

9. Supplementary angles add up to 180º.
40º
120º
60º
140º
Adjacent and Supplementary Angles
Supplementary Angles but not Adjacent

10. Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Angles but not Adjacent

11. Linear Pair: a pair of adjacent angles that measures 180°

12. Perpendicular Lines: intersect to form four right angles

13. Practice Time!

14. Practice Directions: Identify each pair of angles as vertical, supplementary, complementary, linear pair or none of the above.

15. #1
120º
60º

16. #1
120º
60º
Supplementary Angles
Linear Pair

17. #2
60º
30º

18. #2
60º
30º
Complementary Angles

19. #3
75º
75º

20. #3
Vertical Angles
75º
75º

21. #4
60º
40º

22. #4
60º
40º
None of the above

23. #5
60º
60º

24. #5
60º
60º
Vertical Angles

25. #6
135º
45º

26. #6
135º
45º
Supplementary Angles
Linear Pair

27. #7
25º
65º

28. #7
25º
65º
Complementary Angles

29. #8
90º
50º

30. #8
90º
50º
None of the above

31. Directions: Determine the missing angle.

32. #1 ?º
45º

33. #1
135º
45º

34. #2 ?º
65º

35. #2
25º
65º

36. #3 ?º
35º

37. #3
35º
35º

38. #4 ?º
50º

39. #4
130º
50º

40. #5 ?º
140º

41. #5
140º
140º

42. #6 ?º
40º

43. #6
50º
40º

44. Angle Relationship: Investigation 1
The Linear Pair Conjecture
Materials: paper, pencil, 2 sheets of patty paper & protractor
Draw line PQ and place a point R between P and Q.
Choose another point S not on line PQ and draw ray RS. You have just create a linear pair of angles.
Place the “zero edge” of your protractor along line PQ. What do you notice about the sum of the measures of the linear pair of angles?
Compare your results with those of your class. Does everyone make the same observation?
What is the Linear Pair Conjecture?
Example:

45. Angle Relationship: Investigation 2
Vertical Angles Conjectures
Materials: paper, pencil, 2 sheets of patty paper & protractor
Fold patty paper, make a crease, outline the crease, place points A & B on the line.
Fold patty paper again so that you form intersecting lines, make a crease, outline the crease, place points D & E on the line and label the intersection C. (Make sure C is between A & B)
Which angles are vertical angles?
Fold the paper again through point C so that <ACD lies on top of <ECB. What do you notice?
What do you notice about their measures?

46. Angle Relationship Activity p. 54
Your Turn…
Fold through C so that <ACE lies on DCB. What do you notice?
Compare your results with the class.
What is the Vertical Angles Conjecture?
Use a protractor to measure each angles. Write the measures on drawing.
Name the linear pairs. What do you notice about their measures?
Repeat this activity with another piece of patty paper. What do you notice?

47. Practice: complementary and supplementary
Let’s Race!
Find a partner, get a deck of cards, and play “Say it faster!”
Whoever say the complement/supplement faster gets the pair of cards.
The person with the most cards, WINS!
10, Jacks, Queens, Kings, & Aces = 1
Every other find the complement or supplement.

48. Adjacent Practice: Vertical Complementary Supplementary Angle Addition
Complete Angles Relationships
Complete Angle Addition
Quiz will be tomorrow
Study guide tomorrow
Test will be on Friday
Complementary
Supplementary
Angle Addition
Postulate
Linear Pair

49. Warm-Up: Identify each pair of angles Use: adjacent, vertical, complementary, supplementary, and/or linear pair
1. <1 & <2
2. <1 & < 1
3. <4 & <
4. <3 & <4

50. Warm-Up: Find x and each measure2.
(5x + 18)º
(7x + 12)º
3. (10x + 35)º
(13x + 30)º
4. Ray BC is an angle bisector.
Find <CBD & <ABC. A
63º
B C D

51. Warm-Up: Find x and each measure2.
(5x + 18)º
(7x + 12)º

52. Warm-Up: Find x and each measure
4. Ray BC is an angle bisector.
Find <CBD & ABC. A
63º
B C D

53. Warm-Up: Angle Addition
1. The m < ABC = 6x – 8, m < ABD = 3x + 2, and m < DBC = 2x – 1. Find the measure of each angle. A
B D C

54. Warm-Up: A I 3. If m < IBT is 135, find <SBT. C 1 2 S 3 4 T
How to measure and construct angles? How to analyze and measure pairs of angles?
Warm-Up:
A I
C S T
1. Name angle 3.
2. < 3 & <4 are….
3. If m < IBT is 135, find <SBT.
4. <4 = 4x + 5 & <3 = 6x + 5. Find each measure. B

55. Before Test Check study guide Any last minute questions before test
How to measure and construct angles? How to analyze and measure pairs of angles?
Before Test
Check study guide
Any last minute questions before test