1. Angle Relationships
Pre-Algebra

3. Types of Angles Acute Less than 90° Right Exactly 90° Obtuse
Greater than 90°
Straight
Exactly 180°
Reflex
Greater than 180°
Full Rotation
Exactly 360°

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

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

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

7. Complementary Angles sum to 90°
50°
40°

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

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

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

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

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

13. Interior Angles of Polygons
Triangle
Quadrilateral (Square, Rectangle, Parallelogram, Trapezoid)
The sum of the interior angles of any polygon can be found with the following formula using the number of sides.
Sum of Interior angles= (N – 2) x 180
N is the number of sides.

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

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

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

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

35. The End