1. 1.4 – Measure and Classify Angles &
Angle Constructions
1.5 –Describe Angle Pair Relationships

2. Angle:
Two different rays with the same initial point. Measured in degrees. B A 1 C
A,
BAC,
CAB, 1

3. Common initial point, where rays meet pt. A
Vertex
Sides A C B
Common initial point, where rays meet
pt. A
vertex
side A C B
The rays of the angle
side

4. mA = 50° A mR = 90° R mO = 110° O mS = 180° S Acute
Right
Obtuse
Straight
Angle more than 0°, but less than 90° A
mA = 50°
Angle that measures 90°
mR = 90° R
Angle more than 90°, but less than 180°
mO = 110° O
Angle that measures 180°
mS = 180° S

5. Ray that cuts an angle in half to make 2 congruent angles
Angle Bisector
QS bisects PQR
Ray that cuts an angle in half to make 2 congruent angles P S
PQS  SQR Q R

6. Two angles that share a common side and vertex 1 is adjacent to 2
Adjacent angles
Two angles that share a common side and vertex
1 is adjacent to 2 2 1

7. Complementary Angles:
Two angles that add to 90° 1 1 2 2
m1 + m2 = 90°

8. Supplementary Angles:
Two angles that add to 180° 1 1 2 2
m1 + m2 = 180°

9. Linear Pair:
Supplementary angles that are adjacent 1 2
m1 + m2 = 180°

10. Vertical Angles:
Two angles whose sides form two pairs of opposite rays 1 2
They will always be congruent!

11. Angle Addition Postulate:
If you add two adjacent angles, it totals to get their sum. C A B D
mABC + mCBD = mABD

12. 1. Give three names for the angle shown, then name the vertex and sides.
DEF
Pt. E
FED E

13. 1. Give three names for the angle shown, then name the vertex and sides.
QVS
Pt. V
SVQ V

14. 2. Classify the angle as acute, right, obtuse or straight.
mA = 115°
obtuse

15. 2. Classify the angle as acute, right, obtuse or straight.
mA = 90°
right

16. 2. Classify the angle as acute, right, obtuse or straight.
mA = 85°
acute

17. 2. Classify the angle as acute, right, obtuse or straight.
mA = 180°
straight

18. 3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.
91°
obtuse

19. 3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.
32°
acute

20. 3. Use a protractor to find the measure of the angle to the nearest degree. Then classify the angle as acute, obtuse, straight, or right.
180°
straight

21. 4. Find the indicated measure.
mPRS =
81+42
mPRS = 123°

22. 4. Find the indicated measure.
mWXZ =
90 – 26 =
mWXZ = 64°

23. 5. Find each indicated angle.
15°
90°
90°
75°
15°

24. 5. Find each indicated angle.
160°
20°
15°
c = =
15°
a = =
20°
d = =
75°
b = =
160°

25. mNRP + mPRQ = mNRQ
8x x – 1 = 78
12x + 6 = 78
12x = 72
x = 6
mPRQ = 4(6) – 1
mPRQ = 24 – 1
mPRQ = 23°

26. mADB + mBDC = mADC
11x – 7 + 5x – 3 = 118
16x – 10 = 118
16x = 128
x = 8
mADB = 11(8) – 7
mADB = 88 – 7
mADB = 81°

27. 5x + 2 = 7x – 6
2 = 2x – 6
8 = 2x
4 = x
mABC =
5(4)+2 + 7(4)-6 = =
44°

28. 5x + 13 = 9x – 23
13 = 4x – 23
36 = 4x
9 = x
mABC =
5(9) (9)-23 = =
116°

29. 8. Tell whether the indicated angles are adjacent.
EFG and HGF no

30. 8. Tell whether the indicated angles are adjacent.
JNM and MNK
yes

31. 9. Name a pair of complementary angles, supplementary angles, and vertical angles .
ROL and NOP L
LOM and QOP M
Complementary: R N O
QOR and ROL
MON and NOP Q P
Supplementary:
ROL and LON
ROM and MON
QOL and LOM

32. 9. Name a pair of complementary angles, supplementary angles, and vertical angles .
DGE and BGC A
EGB and DGC E
Complementary:
DGE and EGA G B D
Supplementary: C
DGE and EGB
DGA and AGB
EGA and AGC

33. 10. 1 and 2 are complementary angles
10. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m1 = 82°
m2 =
90 – 82 = 8°

34. 10. 1 and 2 are complementary angles
10. 1 and 2 are complementary angles. Given the measure of 1, find m2.
m1 = 23°
m2 =
90 – 23 =
67°

35. 11. 1 and 2 are supplementary angles
11. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
m1 = 82°
m2 =
180 – 82 =
98°

36. 11. 1 and 2 are supplementary angles
11. 1 and 2 are supplementary angles. Given the measure of 1, find m2.
m1 = 105°
m2 =
180 – 105 =
75°

37. 4x + 6 + 11x – 6 = 180 15x = 180 x = 12 4(12)+6 = 48+6 = 54° 11(12)-6
12. Find the measure of ABD and DBC.
4x x – 6 = 180
15x = 180
x = 12
mABD =
4(12)+6
= 48+6
= 54°
11(12)-6
mDBC =
= 132-6
= 126°

38. 12. Find the measure of ABD and DBC.
2x + 3x = 90
5x = 90
x = 18
mABD =
2(18)
= 36°
3(18)
mDBC =
= 54°

39. 13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
1 and 2
Linear pair

40. 13. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
2 and 4
Vertical angles

41. 6. Use the diagram below. Tell whether the angles are vertical angles, linear pair, or neither.
5 and 8
neither

42. 7. Find the values of x and y.
6x – x – 9 = 180
8x – 20 = 180
8x = 200
x = 25°
20y x – 9 = 180
20y (25) – 9 = 180
20y + 60 = 180
20y = 120
y = 6°

43. 7. Find the values of x and y.
9x x + 7 = 180
19x + 9 = 180
19x = 171
x = 9°
18y x + 2 = 180
18y (9) + 2 = 180
18y = 180
18y = 72
y = 4°

44. **Bring compass and ruler tomorrow! Books will not be needed
HW Problem
1.4
1.5
28-32
38-41
4-18 even, 21, 22, 24-27, (draw pic), 40, 41
4, 5, 7-33 odd, 49-52, 61, 62
1.4 # 38
53°
37°
**Bring compass and ruler tomorrow!
Books will not be needed