Transcript 1.4 Angles & their Measures - North Bergen School District

1.4 Angles & their Measures
p. 26
Angle symbol:
• 2 rays that share the same endpoint (or
initial point)
Sides – the rays XY & XZ
Y
5
Z
Named <YXZ, <ZXY (vertex is
always in the middle), or <X (if
it’s the only <X in the diagram).
X
Vertex – the common
endpoint; X
Angles can also be
named by a #. (<5)
There are 3 different <B’s in this diagram;
therefore, none of them should be called <B.
A
<B ?
D
B
C
Angle Measurement
• m<A means the
“measure of <A”
• Measure angles with
a protractor.
• Units of angle
measurement are
degrees (o).
• Angles with the
same measure are
congruent angles.
• If m<A = m<B,
then <A  <B.
Postulate 3: Protractor Post.
• The rays of an angle
can be matched up
with real #s (from 1 to
180) on a protractor
so that the measure
of the < equals the
absolute value of the
difference of the 2 #s.
55o
20o
m<A = 55-20
= 35o
Interior or Exterior?
• B is ___________
in the interior
• C is ___________
in the exterior
on the <
• D is ___________
B
C
D
A
Post. 4: Angle Addition post.
• If P is in the interior of <RST,
then m<QRP + m<PRS = m<QRS.
S
P
If m<QRP=5xo,
m<PRS=2xo, &
m<QRS=84o, find x.
5x+2x=84
Q
7x=84
x=12
m<QRP=60o m<PRS=24o
R
Types of Angles
• Acute angle –
Measures between 0o & 90o
• Right angle –
Measures exactly 90o
• Obtuse angle – Measures between 90o & 180o
• Straight angle – Measures exactly 180o
Adjacent Angles
• 2 angles that share a common vertex &
side, but have no common interior parts.
(they have the same vertex, but don’t
overlap) such as <1 & <2
2
1
Example:
• Name an acute angle
<3, <2, <SBT, or <TBC
• Name an obtuse angle
<ABT
• Name a right angle
<1, <ABS, or <SBC
• Name a straight angle
<ABC
S
T
3
1
2
A
B
C
Assignment