L26 ­ Interior and Exterior Angles of Polygons changes.notebook
May 04, 2017
L26 ­ Angle Relationships in Polygons
Definitions
side lengths are equal and
• regular polygon, all ______________
angles
all ______________
are equal
• examples of regular polygons are equilateral triangles,
squares
• Note the difference between a convex polygon and a
concave polygon
1
L26 ­ Interior and Exterior Angles of Polygons changes.notebook
May 04, 2017
Investigation 1
For each polygon below, draw the diagonals from one vertex.
Count the number of triangles that are formed within the
polygon and record the sum of the interior angles for each
polygon by multiplying the number of triangles by 180.
Record your findings in the table below.
Example
a) triangle
number
of sides
sum of
interior
angles
number
of
triangles (#triangles
x180)
b) quadrilateral
c) pentagon
d) hexagon
a)
3
1
180
b)
4
2
360
c)
5
3
540
d)
6
4
720
e)
7
5
900
f)
8
6
1080
g)
120
118
21240
h)
143
141
25380
i)
157
155
27900
j)
10
8
1440
e) heptagon / septagon
f) octagon
The sum of the interior angles
of a polygon can be
calculated using the formula:
or
2
L26 ­ Interior and Exterior Angles of Polygons changes.notebook
May 04, 2017
Investigation 2
For each regular polygon below, use a ruler to extend one of
the sides as shown in the triangle below. Calculate the
measure of each interior angle by dividing the sum of interior
angles by the number of sides Then calculate the measure of
each exterior angle.
In a polygon, at each vertex, the sum of the exterior angle
and the interior angle is 1800
Example
a)
180­60=120
120
120
3
Attachments
Triangle Relationships.gsp
Interior Angles of Triangle ­ Semi­Circle.gsp
Quadrilateral.gsp
Pentagon.gsp
Hexagon.gsp
Heptagon.gsp
Exterior Angles of Polygon ­ Circle.gsp