1. Angle Relationships & Parallel Lines
Pre-Algebra

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. Complementary Angles sum to 90°
50 °
40 °

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

7. Supplementary Angles sum to 180°
150 °
30 °

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

9. Vertical Angles are opposite one another. Vertical angles are congruent.
100 °
100 °

10. Vertical Angles are opposite one another. Vertical angles are congruent.
80°
80°

11. Lines l and m are parallel. l||m
Note the 4 angles that measure 120°.
120 °
120 ° l
120 °
120 ° m

12. Lines l and m are parallel. l||m
Note the 4 angles that measure 60°.
60°
60° l
60°
60° m

13. Lines l and m are parallel. l||m
There are 4 pairs of angles that are vertical.
There are many pairs of angles that are supplementary.
60°
120 °
120 °
60° l
60°
120 °
120 °
60° m

14. Practice Time!

15. 1) Find the missing angle.?°
36°

16. 1) Find the missing angle.?°
36°
90 ° – 36 = 54°

17. 2) Find the missing angle.?°
64°

18. 2) Find the missing angle.?°
64°
90 ° – 64° = 26°

19. 3) Solve for x.
2x°
3x°

20. 3) Solve for x.
2x°
3x°
3x° + 2x° = 90°
5x = 90
x =18

21. 4) Solve for x.
x + 25
2x + 5

22. 4) Solve for x. x + 25 2x + 5 (2x + 5) + (x + 25) = 90 3x + 30 = 90

23. 5) Find the missing angle.
168 ° ?°

24. 5) Find the missing angle.
168 ° ?°
180° – 168° = 12°

25. 6) Find the missing angle.?°
58°

26. 6) Find the missing angle.?°
58°
180° – 58° = 122°

27. 7) Solve for x. 5x 4x

28. 7) Solve for x. 5x 4x
4x + 5x = 180
9x = 180
x = 20

29. 8) Solve for x.
3x + 20
2x + 10

30. 8) Solve for x. 3x + 20 2x + 10 (2x + 10) + (3x + 20) = 180

31. 9) Lines l and m are parallel. l||m Find the missing angles.
42°
a ° c° b° l d° e° g° f° m

32. 9) Lines l and m are parallel. l||m Find the missing angles.
42°
138 °
138 °
42° l
42°
138 °
138 °
42° m

33. 10) Lines l and m are parallel. l||m Find the missing angles.
81°
a ° c° b° l d° e° g° f° m

34. 10) Lines l and m are parallel. l||m Find the missing angles.
81°
99°
99°
81° l
81°
99°
99°
81° m

35. 11) Find the missing angles.
70 °
70 ° b°
Hint: The 3 angles in a triangle sum to 180°.
d °
65 °

36. 11) Find the missing angles.
70 °
70 °
40°
Hint: The 3 angles in a triangle sum to 180°.
75 °
65 °

37. 12) Find the missing angles.
45 °
50 ° b°
Hint: The 3 angles in a triangle sum to 180°.
d °
75 °

38. 12) Find the missing angles.
45 °
50 °
85°
Hint: The 3 angles in a triangle sum to 180°.
20°
75 °

39. The End