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1.4 – Measure and Classify Angles &
Angle Constructions
1.5 –Describe Angle Pair Relationships
Angle: Two different rays with the same initial
point. Measured in degrees.
B
A
1
C
A, BAC, CAB, 1
B
Common initial
A
Vertex point, where
rays meet
C
pt. A
vertex
side
Sides
The rays of
the angle
B
A
AB
C
side
AC
Acute
Right
Angle more
than 0°, but
less than 90°
Angle that
measures 90°
Obtuse
Angle more
than 90°, but
less than 180°
Straight
Angle that
measures 180°
mA = 50°
A
mR = 90°
R
mO = 110°
O
S
mS = 180°
Ray that
cuts an
P
angle in
Angle
half
to
Bisector
make 2
congruent
Q
angles
QS bisects
PQR
S
R
PQS  SQR
Two angles
Adjacent that share
angles
a common
side and
vertex
2 1
1 is
adjacent to
2
Complementary Angles: Two angles that
add to 90°
1
1
2
m1 + m2 = 90°
2
Supplementary Angles: Two angles that add to
180°
1
1
2
2
m1 + m2 = 180°
Linear Pair: Supplementary angles that
are adjacent
1
2
m1 + m2 = 180°
Vertical Angles: Two angles whose sides form
two pairs of opposite rays
1
2
They will always be congruent!
1  2
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
1. Give three names for the angle shown, then name the
vertex and sides.
Names
Vertex
DEF
FED
E
Pt. E
Sides
ED
EF
1. Give three names for the angle shown, then name the
vertex and sides.
Names
QVS
SVQ
V
Vertex
Pt. V
Sides
VQ
VS
2. Classify the angle as acute, right, obtuse or straight.
mA = 115°
obtuse
2. Classify the angle as acute, right, obtuse or straight.
mA = 90°
right
2. Classify the angle as acute, right, obtuse or straight.
mA = 85°
acute
2. Classify the angle as acute, right, obtuse or straight.
mA = 180°
straight
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
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
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
4. Find the indicated measure.
mPRS = 81+42
mPRS = 123°
4. Find the indicated measure.
mWXZ = 90 – 26 =
mWXZ = 64°
5. Find each indicated angle.
15°
90°
90°
75°
15°
5. Find each indicated angle.
20°
15°
a = 180-160 = 20°
b = 180-20 = 160°
160°
c = 180-90-75 = 15°
d = 180-90-15 = 75°
mNRP + mPRQ = mNRQ
8x + 7 + 4x – 1 = 78
12x + 6 = 78
12x = 72
x=6
mPRQ = 4(6) – 1
mPRQ = 24 – 1
mPRQ = 23°
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°
5x + 2 = 7x – 6
2 = 2x – 6
8 = 2x
4=x
mABC = 5(4)+2 + 7(4)-6 = 20+2 +28-6 = 44°
5x + 13 = 9x – 23
13 = 4x – 23
36 = 4x
9=x
mABC = 5(9)+13 + 9(9)-23 = 45+13+81-23 = 116°
8. Tell whether the indicated angles are adjacent.
EFG and HGF
no
8. Tell whether the indicated angles are adjacent.
JNM and MNK
yes
9. Name a pair of complementary angles, supplementary
angles, and vertical angles .
Vertical:
ROL and NOP
L
M
R
N
O
Q
P
LOM and QOP
Complementary:
QOR and ROL
MON and NOP
Supplementary:
ROL and LON
ROM and MON
QOL and LOM
9. Name a pair of complementary angles, supplementary
angles, and vertical angles .
Vertical:
DGE and BGC
A
EGB and DGC
E
D
G
B
C
Complementary:
DGE and EGA
Supplementary:
DGE and EGB
DGA and AGB
EGA and AGC
10. 1 and 2 are complementary angles. Given the
measure of 1, find m2.
m1 = 82°
m2 = 90 – 82 = 8°
10. 1 and 2 are complementary angles. Given the
measure of 1, find m2.
m1 = 23°
m2 = 90 – 23 = 67°
11. 1 and 2 are supplementary angles. Given the
measure of 1, find m2.
m1 = 82°
m2 = 180 – 82 = 98°
11. 1 and 2 are supplementary angles. Given the
measure of 1, find m2.
m1 = 105°
m2 = 180 – 105 = 75°
12. Find the measure of ABD and DBC.
4x + 6 + 11x – 6 = 180
15x = 180
x = 12
mABD = 4(12)+6
= 48+6
= 54°
mDBC = 11(12)-6
= 132-6
= 126°
12. Find the measure of ABD and DBC.
2x + 3x = 90
5x = 90
x = 18
mABD = 2(18)
= 36°
mDBC = 3(18)
= 54°
13. Use the diagram below. Tell whether the angles
are vertical angles, linear pair, or neither.
1 and 2
Linear pair
13. Use the diagram below. Tell whether the angles
are vertical angles, linear pair, or neither.
2 and 4
Vertical angles
6. Use the diagram below. Tell whether the angles are
vertical angles, linear pair, or neither.
5 and 8
neither
7. Find the values of x and y.
6x – 11 + 2x – 9 = 180
8x – 20 = 180
8x = 200
x = 25°
20y + 19 + 2x – 9 = 180
20y + 19 + 2(25) – 9 = 180
20y + 60 = 180
20y = 120
y = 6°
7. Find the values of x and y.
9x + 2 + 10x + 7 = 180
19x + 9 = 180
19x = 171
x = 9°
18y + 25 + 9x + 2 = 180
18y + 25 + 9(9) + 2 = 180
18y + 108 = 180
18y = 72
y = 4°
HW Problem
1.4
1.5
28-32 4-18 even, 21, 22, 24-27, 33-38 (draw pic), 40, 41
38-41 4, 5, 7-33 odd, 49-52, 61, 62
1.4 # 38
53°
37°
**Bring compass and ruler tomorrow!
Books will not be needed