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Angles In Daily Life
If we look around us, we will see angles everywhere.
Naming An Angle
To name an angle, we name any point on one ray, then the
vertex, and then any point on the other ray.
A
B
C
For example: ABC or CBA
We may also name this angle only by the single letter of the
vertex, for example B.
Adjacent angles are “side by side” and
share a common ray.
15º
45º
These are examples of adjacent
angles.
80º
45º
35º
55º
130º
85º
20º
50º
These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º
Complementary angles add up to 90º.
30º
40º
50º
60º
Adjacent and Complementary
Angles
Complementary Angles
but not Adjacent
Complementary Angles
sum to 90°
50°
40°
1) Find the missing angle.
?°
36°
Supplementary Angles
sum to 180°
30°
150°
Supplementary angles add up to 180º.
40º
120º
60º
Adjacent and Supplementary
Angles
140º
Supplementary Angles
but not Adjacent
6) Find the missing angle.
58°
?°
Congruent Angles
Two angles that have the same measure are called congruent
angles.
D
A
B
300
C
E
300
F
Congruent angles have the same size and shape.
Vertically Opposite Angles
Vertically opposite angles are pairs of angles formed by two
lines intersecting at a point.
C
A
P
B
D
APC = BPD
APB = CPD
Four angles are formed at the point of intersection.
Vertically opposite angles are congruent.
Point of intersection ‘P’ is the common vertex of the four
angles.
Vertical Angles
are opposite one another.
Vertical angles are congruent.
100°
100°
Vertical Angles
are opposite one another.
Vertical angles are congruent.
80°
80°
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
Find the missing angles
Pairs Of Angles Formed by a Transversal
• Corresponding angles
• Alternate angles
• Interior angles
Pairs Of Angles Formed by a Transversal
A line that intersects two or more lines at different points is
called a transversal.
G
A
C
Line L (transversal)
P
B
Line M
Line N
Q
D
F
FourLine
angles
are formed
atMpoint
Pparallel
and
four
point
Line
M and
line
N
areline
lines.P
L intersects
line
and
N another
at point
andatQ.
Eight angles are formed in all by the transversal L.
Q by the transversal L.
Interior and exterior parts
Corresponding angles
When two lines are crossed by the transversal the
angles in matching corners are called corresponding
angles.
Corresponding angles
You need a pair of parallel lines.
corresponding
angles
Draw any line to cut the pair of parallel lines.
What angle is the same as the red one?
How do you tell angles are corresponding?
corresponding
angles
Look for a letter F in any orientation.
Alternate interior angles
• Alternate Interior angles are two
nonadjacent interior angles that lie on
opposite sides of a transversal.
Alternate Exterior angles
Alternate Exterior angles are the angle pairs that are on
the outsides of the two lines (the exterior) and on
opposite (or alternate sides) of the transversal.
Alternate interior angles
You need a pair of parallel lines.
Alternate
interior
angles
Draw any line to cut the pair of parallel lines.
What angle is the same as the blue one?
How do you tell angles are alternate
interior ?
Alternate
interior
angles
Look for a letter Z in any orientation.
Name the pair of alternate interior
and exterior angles?
Practice Time!
Angle 2 measures 110°. What do
the other angles measure?
1.
2.
3. 4.
5. 6.
7. 8.
1) Find the missing angle.
?°
36°
1) Find the missing angle.
?°
36°
1) Find the missing angle.
?°
36°
90 ° – 36 = 54°
2) Find the missing angle.
?°
64°
2) Find the missing angle.
?°
64°
90 ° – 64° = 26°
3) Solve for x.
2x°
3x°
3) Solve for x.
2x°
3x°
3x° + 2x° = 90°
5x = 90
x =18
4) Solve for x.
x + 25
2x + 5
4) Solve for x.
x + 25
2x + 5
(2x + 5) + (x + 25) = 90
3x + 30 = 90
3x = 60
x = 20
5) Find the missing angle.
?°
168°
5) Find the missing angle.
?°
180° – 168° = 12°
168°
6) Find the missing angle.
58°
180° – 58° = 122°
?°
7) Solve for x.
4x
5x
7) Solve for x.
4x
4x + 5x = 180
9x = 180
x = 20
5x
8) Solve for x.
2x + 10
3x + 20