1. Objectives Angle Pair Relationships Adjacent Angles Vertical Angles
Linear Pair
Complementary Angles
Supplementary Angles

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 one another.
75º
105º
105º
75º

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

8. Vertical angles are congruent
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
Two adjacent angles (common vertex and a common ray) that form a straight line. So the two angles add up to ? 180

12. Practice Time!

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

14. #1
120º
60º
Supplementary Angles
And a Linear Pair

15. #2
60º
30º
Complementary Angles

16. #3
Vertical Angles
75º
75º

17. #4
60º
40º
None of the above

18. #5
60º
60º
Vertical Angles

19. Supplementary Angles and a Linear Pair#6
135º
45º
Supplementary Angles and a Linear Pair

20. #7
25º
65º
Complementary Angles

21. #8
90º
50º
None of the above

22. Directions: Determine the missing angle.

23. #1 ?
45º

24. #1
135º
45º

25. #2
65º

26. #2
25º
65º

27. #3
35º

28. #3
35º
35º

29. #4 ?
50º

30. #4
130º
50º

31. #5 ?
140º

32. #5
140º
140º

33. #6 Rectangle ?
40º

34. #6 Rectangle
50º
40º

35. Find angle measures in a linear pair
EXAMPLE
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.

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

37. Find m< AEB
4x +8
6x - 42

38. Write an equation & Solve

39. Find the measure of each <

40. Write an equation & Solve

41. Homework Page 38 # 3 – 42 (x3) and 49 – 52 all
Honors also: # 45, 55, & 56