Download Geom A Unit 1 Day 5 1.4 and 1.5 Angles, Angle Pairs and Their

Geom A Unit 1 Day 5
1.4 and 1.5 Angles, Angle Pairs and Their Measures
I. Angle - ______________________________________________________________________
_______________________________. The symbol for angle is  .
A. The endpoint of the rays is called the ___________________ of the angle.
B. The size of the angle refers to the ___________________ between the rays, not the
length of the sides of the angles.
Name the bigger angle in each pair.
1
B
2
________ is the bigger angle.
A
________ is the bigger angle.
C. When you name an angle, you sometimes can use a number included in the angle (like in the first
eample) or one letter that is the vertex (like the second example), but sometimes, more detail is
needed.
Ex: If we were asked to give the measure for  C in the diagram below, there could be some confusion.
To clear things up, we’d use three letters, the middle one being the point where the angle bends.
A
B
Give each of the following:
38
26
m  ACB = _________
m  BCD = _________
m  ACD = _________
m  BCA = _________
C
D
D. The example above shows us that PART + PART = WHOLE works for angles.
II. Types of Angles and Measuring Angles
A. Measures of angles in this course will be between 0 and 180 .
B. A _________ angle measures 90 .
C. An ________ angles measures less than 90 .
D. An ________ angles measures more than 90 .
E. A _____________ angle measure 180 .
Label each diagram to the right with B, C, D or E to indicate the type of angle drawn.
F. When you are measuring an angle using a protractor, it helps to know ahead of time whether the angle
is ACUTE or OBTUSE.
Tell whether the angle appears to be RIGHT, ACUTE or OBTUSE. Then record its measure.
1.
2.
__________________ ________
____________________ ________
3.
4.
___________________ ________
________________________ ________
III. Angle Addition Examples
A. Remember that two types of angles have implied angle measures that might be needed to
solve certain problems.
1. Right angles = 90
2. Straight angles = 180
H
Q
J



a.
b.
c.

G
D

110
40
P


L
60
45


E
K
N

M
F
Find m  DEF __________
Find m  HJL __________
Find m  QNM __________
B. A big angle made up of two or more parts can be the basis for an equation.
a.  POQ = (x  4)
 QOR = (2 x  2)
 POR = 26
1

x  24 
2

 LMP = x 136
 PMN = 60
b.  LMN = 
P
O
x = __________ m  POQ = _________
Q
P
L

M

R
x = __________ m  LMN = _________

N
II. Pairs of angles:
A. Linear Pair - ___________________________________________________
___________________________________________________
1. Diagram of one linear pair
Informal Observations:
____________ is your straight line.
______________ is an acute angle, it is right
next to _________________, the obtuse
angle, together they make a straight line.
2. Diagram of multiple linear pairs.
A
In the diagram to the right, there are 4 linear
pairs of angles. One is given to you, the next is
started for you. Complete that set and find the
other two.
 AEC
and
 CEB
D
E
C
are a linear pair
 AED and _________ are a linear pair
________ and _________ are a linear pair
________ and _________ are a linear pair
III. Vertical Angles - ____________________________________________________
_____________________________________________________
_____________________________________________________
B
1. Example and Non-Example or Vertical Angles
J
A
F
C
E
H
D
G
B
K
IV. Writing Equations Using Vertical Angles and Linear Pairs of Angles
A. The measures of a linear pair ___________________________________
B. The measures of pair of vertical angles ______________________________
1. Write an equation and solve for each variable.
a)
b)
6 y  80
E
2 y
D
72
A
3x
E
y = _____________
a  60
 4b
H
H
B
2
J
F
C
x = ___________
c.)
1
G
G
J
132
a = ________ b = ________
F
V. Two Pairs of Angles that Don’t Rely on a Diagram
A. Complementary – Any two angles that _____________________________
B. Supplementary – Any two angles that _____________________________
Ex: Find the complement of a 49 angle. ____________
Ex: If  A is 4 times larger than  B, find the measures of both angles,
given that they are supplementary to each other.
HW: Geometry A Unit 1 Day 5 HW