The document defines vocabulary terms related to angle measure including ray, opposite rays, angle, side, vertex, interior, exterior, degree, right angle, acute angle, obtuse angle, and angle bisector. Examples are provided to demonstrate naming angles, measuring angles using a protractor, and solving an equation involving angle measures. The document appears to be notes for a lesson on classifying and measuring different types of angles.

1. Section 1-4
Angle Measure
Monday, September 15, 14

2. Essential Questions
✤ How do you measure and classify angles?
✤ How do you identify and use congruent angles and the bisector of an
angle?
Monday, September 15, 14

3. Vocabulary
1. Ray:
2. Opposite Rays:
3. Angle:
4. Side:
5. Vertex:
6. Interior:
Monday, September 15, 14

4. Vocabulary
1. R a y : Part of a line; has an endpoint and goes on forever in one
direction; ray AB: AB
2. Opposite Rays:
3. Angle:
4. Side:
5. Vertex:
6. Interior:
Monday, September 15, 14

5. Vocabulary
1. R a y : Part of a line; has an endpoint and goes on forever in one
direction; ray AB: AB
2. Opposite Rays: Rays that share an endpoint and are collinear
3. Angle:
4. Side:
5. Vertex:
6. Interior:
Monday, September 15, 14

6. Vocabulary
1. R a y : Part of a line; has an endpoint and goes on forever in one
direction; ray AB: AB
2. Opposite Rays: Rays that share an endpoint and are collinear
3. An g l e : Two noncollinear rays that share an endpoint; uses three points
or a listed number to name ∠ABC or ∠5
4. Side:
5. Vertex:
6. Interior:
Monday, September 15, 14

7. Vocabulary
1. R a y : Part of a line; has an endpoint and goes on forever in one
direction; ray AB: AB
2. Opposite Rays: Rays that share an endpoint and are collinear
3. An g l e : Two noncollinear rays that share an endpoint; uses three points
or a listed number to name ∠ABC or ∠5
4. Side: One of the rays that makes up an angle
5. Vertex:
6. Interior:
Monday, September 15, 14

8. Vocabulary
1. R a y : Part of a line; has an endpoint and goes on forever in one
direction; ray AB: AB
2. Opposite Rays: Rays that share an endpoint and are collinear
3. An g l e : Two noncollinear rays that share an endpoint; uses three points
or a listed number to name ∠ABC or ∠5
4. Side: One of the rays that makes up an angle
5. Vertex: The shared endpoint of the two rays that make up an angle
6. Interior:
Monday, September 15, 14

9. Vocabulary
1. R a y : Part of a line; has an endpoint and goes on forever in one
direction; ray AB: AB
2. Opposite Rays: Rays that share an endpoint and are collinear
3. An g l e : Two noncollinear rays that share an endpoint; uses three points
or a listed number to name ∠ABC or ∠5
4. Side: One of the rays that makes up an angle
5. Vertex: The shared endpoint of the two rays that make up an angle
6. I n t e r i o r : The part of an angle that is inside the two rays of the angle
(the part that is less than 180° in measure)
Monday, September 15, 14

10. Vocabulary
7. Exterior:
8. Degree:
9. Right Angle:
10. Acute Angle:
11. Obtuse Angle:
12. Angle Bisector:
Monday, September 15, 14

11. Vocabulary
7. E x t e r i o r : The part of an angle that is outside the two rays of the
angle (the part that is greater than 180° in measure)
8. Degree:
9. Right Angle:
10. Acute Angle:
11. Obtuse Angle:
12. Angle Bisector:
Monday, September 15, 14

12. Vocabulary
7. E x t e r i o r : The part of an angle that is outside the two rays of the
angle (the part that is greater than 180° in measure)
8. Degree: The unit of measurement of an angle
9. Right Angle:
10. Acute Angle:
11. Obtuse Angle:
12. Angle Bisector:
Monday, September 15, 14

13. Vocabulary
7. E x t e r i o r : The part of an angle that is outside the two rays of the
angle (the part that is greater than 180° in measure)
8. Degree: The unit of measurement of an angle
9. Right Angle: An angle that is 90° in measure
10. Acute Angle:
11. Obtuse Angle:
12. Angle Bisector:
Monday, September 15, 14

14. Vocabulary
7. E x t e r i o r : The part of an angle that is outside the two rays of the
angle (the part that is greater than 180° in measure)
8. Degree: The unit of measurement of an angle
9. Right Angle: An angle that is 90° in measure
10. Acute Angle: An angle that is less than 90° in measure
11. Obtuse Angle:
12. Angle Bisector:
Monday, September 15, 14

15. Vocabulary
7. E x t e r i o r : The part of an angle that is outside the two rays of the
angle (the part that is greater than 180° in measure)
8. Degree: The unit of measurement of an angle
9. Right Angle: An angle that is 90° in measure
10. Acute Angle: An angle that is less than 90° in measure
11. Obtuse Angle: An angle that is more than 90° in measure
12. Angle Bisector:
Monday, September 15, 14

16. Vocabulary
7. E x t e r i o r : The part of an angle that is outside the two rays of the
angle (the part that is greater than 180° in measure)
8. Degree: The unit of measurement of an angle
9. Right Angle: An angle that is 90° in measure
10. Acute Angle: An angle that is less than 90° in measure
11. Obtuse Angle: An angle that is more than 90° in measure
1 2 . A n g l e B i s e c t o r : A ray and splits an angle into two parts with equal
measure
Monday, September 15, 14

17. Example 1
Use the figure.
a. Name all angles that have C as a vertex.
b. Name the sides of ∠7.
c. Write another name for ∠4.
Monday, September 15, 14

18. Example 1
Use the figure.
a. Name all angles that have C as a vertex.
∠ACB,∠BCD,∠DCG,∠GCA
b. Name the sides of ∠7.
c. Write another name for ∠4.
Monday, September 15, 14

19. Example 1
Use the figure.
a. Name all angles that have C as a vertex.
∠ACB,∠BCD,∠DCG,∠GCA
b. Name the sides of ∠7.
DE, DF
c. Write another name for ∠4.
Monday, September 15, 14

20. Example 1
Use the figure.
a. Name all angles that have C as a vertex.
∠ACB,∠BCD,∠DCG,∠GCA
b. Name the sides of ∠7.
DE, DF
c. Write another name for ∠4.
∠IGD
Monday, September 15, 14

21. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
Monday, September 15, 14

22. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
http://www.chutedesign.co.uk/design/protractor/protractor.gif
Monday, September 15, 14

23. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
http://www.chutedesign.co.uk/design/protractor/protractor.gif
Monday, September 15, 14

24. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
http://www.chutedesign.co.uk/design/protractor/protractor.gif
90°, Right
Monday, September 15, 14

25. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
http://www.chutedesign.co.uk/design/protractor/protractor.gif
90°, Right
Monday, September 15, 14

26. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
http://www.chutedesign.co.uk/design/protractor/protractor.gif
90°, Right
Monday, September 15, 14

27. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
http://www.chutedesign.co.uk/design/protractor/protractor.gif
90°, Right
165°, Obtuse
Monday, September 15, 14

28. Example 2
Use the figure. Measure the angles listed and classify as either acute,
right, or obtuse.
a. m∠AFC
b. m∠EFB
c. m∠EFD
http://www.chutedesign.co.uk/design/protractor/protractor.gif
90°, Right
165°, Obtuse
51°, Acute
Monday, September 15, 14

29. Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
Monday, September 15, 14

30. Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
H G J
Monday, September 15, 14

31. B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
H G J
Monday, September 15, 14

32. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
H G J
Monday, September 15, 14

33. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
H G J
Monday, September 15, 14

34. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
H G J
Monday, September 15, 14

35. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
H G J
Monday, September 15, 14

36. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
Monday, September 15, 14

37. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
Monday, September 15, 14

38. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x − 7x
Monday, September 15, 14

39. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
Monday, September 15, 14

40. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
Monday, September 15, 14

41. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
Monday, September 15, 14

42. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
Monday, September 15, 14

43. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
Monday, September 15, 14

44. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7
Monday, September 15, 14

45. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7 = 90 − 7
Monday, September 15, 14

46. R B
Example 3
GH and GJ are opposite rays. GR bisects ∠HGB. If m∠HGR = 9x − 7 and
m∠RGB = 7x + 13, find m∠HGR.
9x − 7
7x + 13
H G J
9x − 7 = 7x + 13
− 7x + 7 − 7x + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7 = 90 − 7 = 83°
Monday, September 15, 14

47. Problem Set
Monday, September 15, 14

48. Problem Set
p. 41 #1-41 odd, 51
“If we all did the things we are capable of doing, we would literally
astound ourselves.” - Thomas A. Edison
Monday, September 15, 14