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Transcript
Adjacent,
Vertical,
Supplementary, and
Complementary Angles
Angles that are “side by side” and share
a common ray are called?
Adjacent angles
15º
45º
These are examples of what type of
angles?
adjacent angles.
80º
45º
35º
55º
130º
85º
20º
50º
These angles are examples of?
Non- Adjacent
100º
50º
35º
35º
55º
45º
When 2 lines intersect, they make what
type of angles?
vertical angles
75º
105º
105º
75º
What type of angles are opposite one
another?
Vertical angles
75º
105º
105º
75º
Vertical angles are opposite one
another. What is the measure of angle
A?
75º
A
105º
75º
Vertical angles are?
congruent (equal).
150º
30º
30º
150º
Supplementary angles add up to? 180º
40º
120º
60º
Adjacent and Supplementary
Angles
140º
Supplementary Angles
but not Adjacent
Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary
Angles
Complementary Angles
but not Adjacent
Angles Around a Point
Angles around a point will always add up to
360 degrees.
The angles above all add to 360°
53° + 80° + 140° + 87° = 360°
Practice Time!
Directions:
Identify each pair of angles as
vertical, supplementary,
complementary,
or none of the above.
#1
120º
60º
#1
120º
60º
Supplementary Angles
#2
30º
60º
#2
30º
60º
Complementary Angles
#3
75º
75º
#3
Vertical Angles
75º
75º
#4
40º
60º
#4
40º
60º
None of the above
#5
60º
60º
#5
60º
60º
Vertical Angles
#6
135º
45º
#6
135º
45º
Supplementary Angles
#7
25º
65º
#7
25º
65º
Complementary Angles
#8
90º
50º
#8
90º
50º
None of the above
Now, think of what we talked about today.
1
5
2
4
3
Are angles 4 and 5 supplementary angles?
no
Are angles 2 and 3 complementary angles?
no
Are angles 4 and 3 supplementary angles?
yes
Are angles 2 and 1 complementary angles?
yes
Name the adjacent angles and linear pair of angles in the
given figure:
Adjacent angles:
ABD and DBC
A
ABE and DBA
00
30
30
Linear pair of angles:
EBA, ABC
EBD, DBC
0 0
9090
E
D
0
60
600
B
C
Name the vertically opposite angles and adjacent angles in
the given figure:
C
A
P
B
D
Vertically opposite angles: APC and BPD
Adjacent angles: APC and CPD
APB
and CPD
APB
and BPD
Pairs Of Angles Formed by a Transversal
• Corresponding angles
• Alternate angles
• Interior angles
Corresponding Angles
When two parallel lines are cut by a transversal, pairs of
corresponding angles are formed.
L
Line L
GPB = PQE
G
A
D
P
B
Q
E
F
Line M
Line N
GPA = PQD
BPQ = EQF
APQ = DQF
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
Alternate Angles
Alternate angles are formed on opposite sides of the
transversal and at different intersecting points.
L
G
A
D
Line L
P
B
Q
E
Line M
Line N
BPQ = DQP
APQ = EQP
F
Two pairs of alternate angles are formed.
Pairs of alternate angles are congruent.
Interior Angles
The angles that lie in the area between the two parallel lines
that are cut by a transversal, are called interior angles.
L
G
A 120
Line L
0P
600
E
Line N
APQ + DQP = 1800
1200
600
D
B
Line M
BPQ + EQP = 1800
Q
F
interior
eachside
pairofadd
AThe
pairmeasures
of interiorofangles
lieangles
on the in
same
theup to 1800.
transversal.
Name the pairs of the following angles formed by a
transversal.
GG
G
AA
500
Line
Line
Line LL
L
P P
BBB
1300
D
DD
Q
Q
Q
EEE
FFF
Line
Line
Line
MM M
Line
Line
N
Line
NN
Directions:
Determine the missing angle.
#1
?º
45º
#1
135º
45º
#2
?º
65º
#2
25º
65º
#3
?º
35º
#3
35º
35º
#4
?º
50º
#4
130º
50º
Find the value of x.
x
x + 15 = 90
x = 75
15
#5
?º
140º
#5
140º
140º
Find the value of x.
(4x + 3)
(x - 8)
(4x + 3) + (x - 8) = 90
5x - 5 = 90
5x = 95
x = 19
#6
?º
40º
#6
50º
40º