8.1 Classifying Polygons

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8.2 Angles in Polygons
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Polygon Number of sides Number of triangles Sum of measures of interior angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
3
1
1180180
4
2
2180360
5
3
3180540
4180720
6
4
7
5
5180900
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Angle Review

• Polygons have two types of angles
• Interior angles
• Exterior angles

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Interior or Exterior?
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Theorem 8.1

• The sum of the measures of the interior angles of
  a convex polygon with n sides is

2
3
1
4
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Example

• Find the measure of the interior angle of a
  regular hexagon.

The sum of the measures of the hexagon is
Since the hexagon is regular, each angle has the
same measure. Hence, divide by 6 to find the
measure of one angle.
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Example

• Find the measure of angle E.

A
B
E
C
D
Find the sum of the measures of any pentagon.
Subtract the sum of the given angles from this
total.
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Theorem 8.2

• The sum of the measures of the exterior angles of
  a convex polygon, one angle at each vertex, is
  360.

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Example

• Find the value of x.

75
44
65
54
x
76
6544755476314
360-31446