The document defines various terms related to angle measure including ray, angle, vertex, acute angle, obtuse angle, and angle bisector. It then provides examples measuring angles in a figure and solving an equation involving angle measures.

1. Section 1-4
Angle Measure

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

3. Vocabulary
1. Ray:
2. Opposite Rays:
3. Angle:
4. Side:
5. Vertex:
6. Interior:

4. Vocabulary
1. Ray: 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:

5. Vocabulary
1. Ray: 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:

6. Vocabulary
1. Ray: 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: 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:

7. Vocabulary
1. Ray: 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: 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:

8. Vocabulary
1. Ray: 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: 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:

9. Vocabulary
1. Ray: 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: 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:The part of an angle that is inside the two rays of the angle
(the part that is less than 180° in measure)

10. Vocabulary
7. Exterior:
8. Degree:
9. Right Angle:
10. Acute Angle:
11. Obtuse Angle:
12. Angle Bisector:

11. Vocabulary
7. Exterior: 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:

12. Vocabulary
7. Exterior: 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:

13. Vocabulary
7. Exterior: 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:

14. Vocabulary
7. Exterior: 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:

15. Vocabulary
7. Exterior: 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:

16. Vocabulary
7. Exterior: 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: A ray and splits an angle into two parts with equal
measure

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.

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.

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.

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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.
H G J
9x − 7

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.
H G J
9x − 7
7x + 13

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7
2x = 20

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7
2x = 20
2 2

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7
2x = 20
2 2
x = 10

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7 = 90 − 7

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.
H G J
9x − 7
7x + 13
9x − 7 = 7x + 13
− 7x− 7x + 7 + 7
2x = 20
2 2
x = 10
m∠HGR = 9(10) − 7 = 90 − 7 = 83°