Transcript 3-4 The Polygon Sum Theorem

L.E.Q. How do you find the sums of the
measures of the interior and exterior angles of
polygons?

A closed figure in a plane, formed by
connecting line segments at their endpoints
with each segment intersecting exactly 2
others.

List the vertices in
consecutive order.
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You can name this
pentagon ABCDE.
What are some other
ways you can name
it?
What is an incorrect
way to name it?
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A line segment that connects 2
nonconsecutive vertices.
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Convex Polygons - All diagonals are inside,
no diagonal could be outside the polygon.
Concave Polygons – At least one diagonal
could be on the outside of the polygon.

Divide the polygon into triangles with a
common vertex.
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Multiply the number of triangles by 180
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(n – 2) 180° where n
= the number of
sides of the polygon.
In this case n = 6
= (6 – 2)180°
= (4) 180°
= 720°

Find the sum of the measures of the angles of
a 15-gon.
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Find the measure of the missing angle.
140°
89°
75°
X
123°
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The sum of the measures of the exterior
angles of a polygon, one at each vertex, is
360 degrees.

Find the measure of the missing angle.
X
70°
86°
83°
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A polygon where all the sides have the same
length.

A polygon where all the angles have the same
measure.

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A polygon where all the angles are equal and
all of the sides are the same length.
They are both equilateral and equiangular
Examples of Regular
Polygons
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Pgs. 147-149 #s 2-24 even, 32-35 all, 4044 all, 47-49 all.