1. ANGLES

2. You will learn to classify angles as acute, obtuse, right, or straight.

3. What is an angle?
Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

4. Here are some examples
of angles.

5. We can identify an angle by using a point on each ray and the vertex
We can identify an angle by using a point on each ray and the vertex. The angle below may be identified as angle ABC or as angle CBA; you may also see this written as ABC or as CBA. The vertex point is always in the middle.

6. Protractor
A device used to measure angles.

7. Angle Measurements We measure the size of an angle using degrees.
Here are some examples of angles and their degree measurements.

8. Acute Angles
An acute angle is an angle measuring between 0 and 90 degrees.
The following angles are all acute angles.

9. Obtuse Angles
An obtuse angle is an angle measuring between 90 and 180 degrees.
The following angles are all obtuse.

10. Right Angles A right angle is an angle measuring 90 degrees.
The following angles are both right angles.

11. Straight Angle
A straight angle is 180 degrees.

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

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

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

15. Two angles are called supplementary angles if the sum
of their degree measurements equals 180 degrees.
Example:
These two angles are supplementary.
                                                                      

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

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

18. Vertical Angles
For any two lines that meet, such as in the diagram below,
angle AEB and angle DEC are called vertical angles.
Angle BEC and angle AED are also vertical angles.
Vertical angles have the same degree measurement.                                    
110 70 70
110

19. Adjacent, Vertical, Angles

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

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

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

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

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

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

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

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

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