Sec' 1 6 Measuring Angles

1
Sec. 1 6 Measuring Angles

• Objectives
• 1) Find the measures of angles.

2
Geometry vs Algebra

• Segments are Congruent
• Symbol ?
• AB ? CD
• ?1 ? ?2
• Lengths of segments are equal.
• Symbol
• AB CD
• m?1 m?2

3
Angles

• Formed by 2 rays with the same endpoint
• Vertex of the Angle
• Symbol ?
• Name it by
• Its Vertex ?A
• A number ?1
• Or by 3 Points ?BAC
• Vertex has to be in the middle

B
1
A
C
4

• Ex.5 How many ?s can you find? Name them.
• 3 ?s
• ?ADB or ?BDA
• ?BDC or ?CDB
• ?ADC or ?CDA
• Notice D (the vertex) is always in the middle.
• Cant use ?D
• But ?1 or ?2 could be added.

B
A
1
C
2
D
5
Classifying Angles by their Measures
Acute ?
Right ?
Obtuse ?
x
x
x
x lt 90
x 90
x gt 90
x
Straight ?
x 180
6
Protractor Postulate

• P (1 7) Let OA OB be opposite rays in a
  plane, all the rays with endpoint O that can be
  drawn on one side of AB can be paired with the
  real number from 0 to 180.

C
D
A
B
O
7
Angle Addition Postulate

• If point B is in the interior of ?MAD, then
• m?MAB m?BAD m?MAD

B
M
D
A
8

• If ?MAD is a straight ?, then
• m?MAB m?BAD m?MAD 180

B
D
M
A
9
Ex.6 Finding ? measures

• Find m?TSW if
• m?RSW 130
• m?RST 100

W
T
R
S
m?RST m?TSW m?RSW 100 m?TSW 130 m?TSW
30
10

• ? Addition
• m?XYZ 150

x
?1 3x - 15
?2 2x - 10
Z
Y
m?1 m?2 m?XYZ (3x - 15) (2x 10) 150 5x
25 150 5x 175 x 35
11

1-4
12

Use the Angle Addition Postulate to solve.
1-4
13
Name all pairs of angles in the diagram that
are a. vertical
Vertical angles are two angles whose sides are
opposite rays. Because all the angles shown are
formed by two intersecting lines, ?1 and ?3 are
vertical angles, and ?2 and ?4 are vertical
angles.
b. supplementary
14
(continued)
c. complementary
Two angles are complementary if the sum of their
measures is 90. No pair of angles is
complementary.
1-6
15
Use the diagram below. Which of
the following can you conclude ?3 is a right
angle, ?1 and ?5 are adjacent, ?3 ?5?
You can conclude that ?1 and ?5 are adjacent
because they share a common side, a common
vertex, and no common interior points.
Although ?3 appears to be a right angle, it is
not marked with a right angle symbol, so you
cannot conclude that ?3 is a right angle.