Download 1.4 - Madison County Schools

1.4 INTRO TO ANGLE
MEASUREMENT
Measuring Angles
• Angles are measured using a protractor, which
looks like a half-circle with markings around
its edges.
• Angles are measured in units called degrees
• 45 degrees, for example, is symbolized like
this: 45
• Every angle on a protractor measures more
than 0 degrees and less than or equal to 180
degrees.
2
A Protractor
3
• The smaller the opening between the two
sides of an angle, the smaller the angle
measurement.
• The largest angle measurement (180
degrees) occurs when the two sides of
the angle are pointing in opposite
directions.
• To denote the measure of an angle we
write an “m” in front of the symbol for
the angle.
4
• Here are some common angles and
their measurements.
m1  45
1
m2  90
2
m3  135
3
4
m4  180
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Types of Angles
• An acute angle is an angle that measures
less than 90 degrees.
• A right angle is an angle that measures
exactly 90 degrees.
• An obtuse angle is an angle that measures
more than 90 degrees.
acute
right
obtuse
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• A straight angle is an angle that measures
180 degrees. (It is the same as a line.)
• When drawing a right angle we often mark its
opening as in the picture below.
right angle
straight angle
7
Adjacent Angles
• Adjacent Angles
share a RAY and a
VERTEX but no
INTERIOR POINTS.
• Angles x and y do
not share a ray.
• <DOC is adjacent to
<COB, but it is not
adjacent to <DOB.
Can you tell why?
(think about Point C)
Angles and Their Parts
• An angle consists of two
different rays that have the
same initial point. The rays
are the sides of the angle.
The initial point is the
vertex of the angle.
• Point M is on the INTERIOR
of <CAB.
• Point Q is on the
EXTERIOR of <CAB.
• Point A is the VERTEX.
vertex
• Points A, C, and B sit ON
the angle.
• Rays: AC and AB make up
the angle
•Q
C
•M
sides
B
A
Note:
• The measure of A is denoted by mA.
The measure of an angle can be
approximated using a protractor, using
units called degrees(°). For instance,
BAC has a measure of 50°, which can
be written as
B
mBAC = 50°.
A
C
Reading a protractor.
A
O
What m<BOA?
103°
B
Naming Angles
• We could name this
angle using the
points or the number
at the vertex.
1
• There are 4 names
we could this angle—
• <E—since point E is
the vertex and there
is ONLY ONE angle
using that vertex.
• <FED or <DEF—
notice that the vertex
is the middle point
mentioned.
• <1—for the number
given at the vertex.
Angle Addition Postulate
• If C is in the interior
of <ABD, then
m<ABC + m<CBD =
m<ABD.
• In other words, little
angle + little angle =
big angle.
Angle Addition Post., Continued
• m<CAB + m<DAC =
m<DAB, so…
• m<CAB + 53° = 64°
• m<CAB = 11°
• Find the m<DAB.
• m<DAC + m<CAB =
m<DAB.
• 35° + 30° = 65°
• If m<ABM = (3x + 2)° and m<MBC = (5x-4)° and
m<ABC = 102°, find x and the angle measures.
• Angle Addition Postulate:
• m<ABM + m<MBC = m<ABC
• 3x + 2 + 5x – 4 = 102
(use subst.)
• 8x – 2 = 102
(CLT)
• 8x = 104
(Add. POE)
• x = 13
(Div. POE)
• m<ABM = 41°; m<MBC = 61°