1. 1.4: Measure and Classify Angles
Objectives:
To define, classify, draw, name, and measure various angles
To use the Protractor and Angle Addition Postulates
To construct congruent angles and angle bisectors with compass and straightedge
To convert angle measurement between degrees and radians

2. Vocabulary Angle Obtuse  Vertex Right  Sides Straight  Acute 
In your notes, define each of these without your book. Draw a picture for each word and leave a bit of space for additions and revisions.
Angle
Obtuse 
Vertex
Right 
Sides
Straight 
Acute 
Congruent ’s

3. A “Rabbit Ear” antenna is a physical model of an angle
An angle consists of two different rays (sides) that share a common endpoint (vertex).
Angle ABC, ABC, CBA or B
The vertex is the key
Vertex
Sides
A “Rabbit Ear” antenna is a physical model of an angle

4. Angle
Each angles creates 2 regions: INTERIOR and EXTERIOR.

5. Example 1
How many angles can be seen in the diagram? Name all the angles. 3
< WXY, < YXZ, <WXZ

6. 1.4 Measure and Classify Angles
How Big is an Angle?
Is the angle between the two hands of the wristwatch smaller than the angle between the hands of the large clock?
Both clocks read 9:36
Click me to learn more about measuring angles

7. Measure of an Angle
The measure of an angle is the smallest amount of rotation about the vertex from one side to the other, measured in degrees.
Can be any value between 0 and 180
Measured with a protractor

8. Classifying Angles
Surely you are familiar with all of my angular friends by now.

9. How To Use a Protractor The measure of this angle is written:
Click the button to see how to measure an angle.
The measure of this
angle is written:

10. Example 2 Complete your Protractor Practice worksheet.
Write your answer in the form
Draw your angles on the back and label them something!

11. Example 3
What is the measure of DOZ?
650

12. Example 3
You basically used the Angle Addition Postulate to get the measure of the angle, where mDOG + mGOZ = mDOZ.

13. Angle Addition Postulate
If P is in the interior of RST, then mRST = mRSP + mPST.

14. Example 4 Given that mLKN = 145°, find mLKM and mMKN.
Set up an equation and solve
X = 23
<LKM = 56
<MKN = 89
CHECK: = 145

15. markings to your picture.
Congruent Angles
Two angles are congruent angles if they have the same measure.
Add the appropriate
markings to your picture.

16. Congruent Angles
Draw angle A in your notebook. How could you copy that angle to another part of your paper using only a
compass and a
straightedge?

17. Congruent Angles
Draw angle A.

18. Congruent Angles
Draw a ray with endpoint A’.

19. Congruent Angles
Put point of compass on A and draw an arc that intersects both sides of the angle. Label these points
B and C.

20. Congruent Angles
Put point of compass on A’ and use the compass setting from Step 3 to draw a similar arc on the ray.
Label point B’ where
the arc intersects
the ray.

21. Congruent Angles
Put point of compass on B and pencil on C. Make a small arc.

22. Congruent Angles
Put point of compass on B’ and use the compass setting from Step 5 to draw an arc that intersects the
arc from Step 4.
Label the
new point
C’.

23. Congruent Angles
Draw ray A’C’.

24. Congruent Angles
Click on the button to watch a video of the construction.

25. Angle Bisector
An angle bisector is a ray that divides an angle into two congruent angles.

26. Bisect an Angle
Draw an acute angle and label the vertex A.

27. Bisect an Angle
Using vertex A as the center, draw an arc intersecting both sides of your angle. Label the intersections B and C.

28. Bisect an Angle
Using the same compass setting, draw two intersecting arcs in the interior of your angle, one centered at B, the other centered at C.

29. Bisect an Angle
Label the intersection D.

30. Bisect an Angle
Draw a ray from vertex A through point D.

31. Angle Bisector: Video
Click on the button to watch a video of the construction.

32. Example 5
In the diagram, YW bisects XYZ, and mXYW = 18°. Find mXYZ.
360

33. Example 6
In the diagram, OE bisects angle LON. Find the value of x and the measure of each angle.
Set up and equation and solve.
X = 3
Both angles are 38

34. Radians
You can also measure an angle in radians. Radians are like the less well-known greasy, nerdy-type who eats lots of pie.

35. 1.4 Measure and Classify Angles
Radians
One radian is the measure of the angle formed by stretching the radius of a circle around its circumference.

36. 1.4 Measure and Classify Angles
Example 7
How many radians would be the equivalent to one full revolution around the unit circle? How many radians would equal 180°?

37. Example 8
Use the conversion factor 180° =  radians to convert the following angle measures.
Convert 27° into radians.
 = ?
Convert rad into degrees.
27 π
180
3  20
 = 3/4π ?
? = 135