Download special types of angles

Special Types of Angles
Objectives:
…to determine measures of complementary, supplementary, and vertical
angles
…to name or identify complementary, supplementary, adjacent, and vertical
angles
...to name, identify and/or determine measures of alternate interior, alternate
exterior, and corresponding angles
Assessment Anchor:
8.C.1.1 – Identify, use and/or describe properties of angles, triangles,
quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones, and/or cylinders.
Vocabulary alert!!
COMPLEMENTARY ANGLES – two angles whose
measures add up to 90°
SUPPLEMENTARY ANGLES – two angles whose
measures add up to 180°
EXAMPLES
∠ BAD and ∠ DAC
∠ ROT and ∠ SOT
are complementary angles.
B
D
A
C
are supplementary angles.
T
S
O
R
∠ GHF is complementary to _________
∠ GHF is supplementary to _________
D
E
F
∠ CHD is supplementary to _________
∠ EHD is complementary to _________
C
H
G
Special Types of Angles
(Without a picture)
What is the complement of a 54° angle?
Calculation
90 – 54 =
Answer
36°
What is the supplement of a 112° angle?
180 – 112 =
68°
What is the complement of a 19° angle?
90 – 19 =
_____
What is the supplement of an 81° angle?
__________
_____
What is the complement of a 37° angle?
__________
_____
What is the supplement of an 18° angle?
__________
_____
***What is the complement of a 93° angle?
__________
_____
***What is the supplement of a 211° angle?
__________
_____
***If m ∠ A = 28°, m ∠ B = 48°, and m ∠ C = 14°…
can we call these angles complementary angles? _______________________
Vocabulary alert!!
ADJACENT ANGLES – two angles that share a vertex and
a side, but no interior points
VERTICAL ANGLES – two angles formed by intersecting
lines and are opposite each other
**Vertical angles are congruent
EXAMPLES
∠ WAY and ∠ XAZ
W
A
are vertical angles.
∠ WAX and ∠ WAY
X
Z
Y
are adjacent angles.
∠ 1 and ∠ 3 are vertical angles.
∠ 2 and ∠ 3 are adjacent angles.
1
2
4
3
Special Types of Angles
IF m ∠ FTE = 41°, then...
C
m ∠ BTD = _____
m ∠ CTF = _____
m ∠ ATB = _____
m ∠ ATE = _____
D
F
T
E
B
A
m ∠ CTD = _____
IF m ∠ 5 = 71°, then...
m ∠ 2 = _____
m ∠ 1 = _____
m ∠ 4 = _____
1
m ∠ 6 = _____
2
3
6
5
4
m ∠ 3 = _____
Write an equation using ∠ ABD and
∠ DBC. Then solve for “x”.
A
D
(3x – 14)°
(2x + 9)°
B
m ∠ ABD = _____
Write an equation using ∠ RAS and
∠ TAV. Then solve for “x”.
C
m ∠ DBC = _____
R
S
(5x – 18)°
A
T
(4x + 7)°
V
m ∠ RAS = _____
m ∠ SAV = _____
Special Types of Angles
Vocabulary alert!!
TRANSVERSAL – a line that intersects two other lines at
two different points
CORRESPONDING ANGLES – non-adjacent angles that lie
on the same side of the
transversal and in
corresponding positions
ALTERNATE INTERIOR ANGLES – angles that are on
opposite sides of the
transversal, and are
two lines
Transversal: a line that intersects two other linesbetween
in differentthe
points
Corresponding
angles thatANGLES
lie on the same
side of the
ATERNATEangles:
EXTERIOR
– angles
thattransversal
are on and in
corresponding positions
Alternate Interior angles:
opposite sides of the
transversal,
are and
angles that lie on opposite
sides of theand
transversal
in the interior of the pair
of linesthe two lines
outside
*** When a transversal intersects two PARALLEL lines… corresponding
angles are congruent AND alternate interior angles are congruent AND
alternate exterior angles are congruent!!
EXAMPLES
Line p is a transversal.
Pairs of corresponding angles:
∠ 1 and ∠ 5
∠ 2 and ∠ 6
∠ 3 and ∠ 7
∠ 4 and ∠ 8
p
m
1
4
n
2
3
5
Pairs of alternate interior angles:
∠ 2 and ∠ 8
∠ 3 and ∠ 5
Pairs of alternate exterior angles:
∠ 1 and ∠ 7
∠ 4 and ∠ 6
8
6
7
Special Types of Angles
IF m ∠ 4 = 114°, then...
m ∠ 1 = _____
Lines a and b are parallel.
m ∠ 6 = _____
1
2
a
m ∠ 2 = _____
m ∠ 7 = _____
m ∠ 3 = _____
m ∠ 8 = _____
3
5
4
6
b
m ∠ 5 = _____
7
c
8
Lines m and n are parallel.
1
Write an equation using ∠ 2
and ∠ 4. Then solve for “x”.
(7x + 35)°
m
3
(3x – 5)°
5
6
n
7
8
y
m ∠ 7 = _____
m ∠ 8 = _____
Lines p and q are parallel.
Write an equation using ∠ 2 and
and ∠ 6. Then solve for “x”.
p
q
7
(5x – 27)°
5 8
3
(3x + 31)°
1 4
h
m ∠ 7 = _____
m ∠ 8 = _____