5A Angles

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5A Angles
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Straight Lines
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An Angle

• A figure formed by two rays with the same endpoint

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Angles
VERTEX
MEASURE
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Acute Angle

• An angle with a measure less than a right angle

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Right angle

• An angle, or square corner, formed by
  perpendicular lines.

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Obtuse angle

• An angle with a measure that is greater than a
  right angle.

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There are 3 types of angles
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Angles
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A REFLEX ANGLE is one whose measure is GREATER
THAN 180 AND LESS THAN 360 DEGREES.
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Right triangle Has one 90 degree angle
                             Equilateral
triangle All angles are the same (60 degrees)
                          Isosceles triangle
Has two angles the same and two sides the same
                        
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                         Scalene triangle
Has all three angles and all three sides
different                                     
                  Obtuse triangle Has one
obtuse angle, greater than 90 degrees
                                                  
                            
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Angles
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A LINEAR PAIR of angles are adjacent angles who
non common sides are oppposite rays.  The sum of
the measures of the angles in a linear pair is
180.
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SUPPLEMENTARY ANGLES - If the sum of the measures
of two angles is 180 degrees, then the angles are
supplementary.  (One angle is the supplement of
the other.) So you ask how is this different from
a linear pair, well a linear pair must be
adjacent angles whereas supplementary angles do
not have to be, although they often are as in the
diagram below.
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Find the value of x.
x
30
x 30 180
- 30 - 30
x 150
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COMPLEMENTARY ANGLES - If the sum of the measures
of two angles is 90 degrees, then the angles are
complementary.  (One angle is the complement of
the other.)
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Angles are formed when 2 lines meet
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VERTICAL ANGLES are two nonadjacent angles formed
by two intersecting lines. (These can be found by
the X that the two intersecting lines form)
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Vertical Angles Theorem
- the opposite angles of intersecting lines must
be equal.
Find the missing angles a, b and c.
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155
b
c
a
155
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Angles and Parallel Lines
180 - q
q
q
180 - q
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geo angles
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Given angle BAM is a right angle, angle TAP
equals 95o and angle MAP equals 60o, find the
measurement of all angles in this figure.
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Given segment ZB perpendicular to AM and ZP and
parallel to TM.  Given triangle ZXN is
isosceles.  If angle NZX equals 65o, find all
other angles in this figure
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- the sum of the interior angles of any triangle
is always 180 .
180 Rule for Triangles
b
80
x
40
a
c
40 80 x 180
120 x 180
x 60
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All the angles of a triangle add up to 180
degrees. So if you have this triangle
                                                  
                
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ADJACENT ANGLES are angles in the same plane,
that have a common vertex and a common side, but
no common interior points.   In the diagram HKF
and FKI share vertex K and side KF.
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Find the missing angle.
x
40
132
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Find the missing angle.
119
124
x
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Lines/Angles
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angles
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Measuring Angles
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Math A - Angles
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Geometry Experimentation
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Ball Physics 
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Math Pool Table  
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Pool Table 
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