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.
Complementary angles: two angles whose measurements sum up to be 90°
Supplementary angles: two angles whose measurements sum up to be 180°
NOTES
From a picture:
∠ BAD and ∠ DAC
are complementary angles.
B
D
Reminder: _________________
A
C
∠ ROT and ∠ SOT
are supplementary angles.
T
Reminder: _________________
S
O
R
Special Types of Angles
EXAMPLES
∠ GHF is complementary to _________
∠ GHF is supplementary to _________
D
E
∠ CHD is supplementary to _________
F
∠ EHD is complementary to _________
C
H
G
MORE EXAMPLES
Without a picture:
Calculation
Answer
What is the complement of a 54° angle?
90 – 54 =
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 supplement of a 145° angle?
__________
_____
What is the complement of a 76° 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?
Special Types of Angles
Vertical angles: two angles formed by two intersecting lines, and are opposite
each other
Adjacent angles: two angles that share a vertex and a side but no interior points
**** Vertical angles are always congruent!! (same measure)
NOTES
W
X
∠ WAY and ∠ XAZ
are vertical angles.
A
Z
∠ WAX and ∠ WAY
Y
are adjacent angles.
∠ 1 and ∠ 3
are vertical angles.
1
∠ 2 and ∠ 3
2
4
are adjacent angles.
3
EXAMPLES
IF m ∠ FTE = 41°, then...
m ∠ BTD = _____
m ∠ CTF = _____
m ∠ ATB = _____
m ∠ ATE = _____
m ∠ CTD = _____
C
D
T
B
A
F
E
Special Types of Angles
IF m ∠ 5 = 71°, then...
m ∠ 2 = _____
1
m ∠ 1 = _____
2
3
6 5
4
m ∠ 4 = _____
m ∠ 3 = _____
m ∠ 6 = _____
1. Write an equation using ∠ ABD and
∠ DBC. Then solve for “x”.
A
D
(3x – 14)°
B
2. m ∠ ABD = _____
(2x + 9)°
C
m ∠ DBC = _____
1. Write an equation using ∠ RAS and
∠ TAV. Then solve for “x”.
R
S
(5x – 18)°
A
T
(4x + 7)°
V
2. m ∠ RAS = _____
m ∠ SAV = _____
Special Types of Angles
Transversal: a line that intersects two other lines in different points
Corresponding angles: angles that lie on the same side of the transversal and in
corresponding positions
Alternate Interior angles: angles that lie on opposite sides of the transversal and
in the interior of the pair of lines
**** When a transversal intersects two PARALLEL lines, corresponding
angles are congruent AND alternate interior angles are congruent!!
NOTES
m
Line p is a transversal.
1
n
2
Pairs of corresponding angles:
∠ 1 and ∠ 5
∠ 2 and ∠ 6
∠ 3 and ∠ 7
∠ 4 and ∠ 8
4 3
5
8
6
7
p
Pairs of alternate interior angles:
∠ 2 and ∠ 8
∠ 3 and ∠ 5
EXAMPLES
Lines a and b are parallel.
1
2
IF m ∠ 4 = 114°, then...
a
3
m ∠ 1 = _____
m ∠ 6 = _____
5
m ∠ 2 = _____
m ∠ 5 = _____
6
m ∠ 7 = _____
b
7
m ∠ 3 = _____
4
m ∠ 8 = _____
c
8
Special Types of Angles
Lines m and n are parallel.
1
2
IF m ∠ 5 = 39°, then...
m
3
m ∠ 1 = _____
4
m ∠ 6 = _____
5
m ∠ 2 = _____
6
m ∠ 7 = _____
n
7
m ∠ 3 = _____
8
m ∠ 8 = _____
y
m ∠ 4 = _____
Lines p and q are parallel.
1. Write an equation using ∠ 2 and ∠ 6.
Then solve for “x”.
p
q
7
(5x – 27)°
5 8
3
(3x + 31)°
1 4
h
2. Find the remaining measures.
m ∠ 1 = _____
m ∠ 5 = _____
m ∠ 3 = _____
m ∠ 7 = _____
m ∠ 4 = _____
m ∠ 8 = _____