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Name: _____________________________
Geometry
Ch. 6.1: Angles of Polygons
We will now be moving from studying the properties of triangles to studying the properties of quadrilaterals.
Polygon: A ________ figure formed by a finite
number of coplanar _____________ called sides such
that:

The sides that have a common endpoint are
_________________

Each side intersects exactly ________ other
sides but only at the _____________
Diagonal of a Polygon: A segment that connects any
two nonconsecutive vertices
Find an expression for the sum of the angles of an n-sided convex polygon.
Number
of sides
(n)
Sum of
interior
angles (s)
Theorem 6.1: The sum of the interior angle measures of an n-sided convex polygon is ___________________
Example: What is the sum of the angle measures of a 27-gon?
Name: _____________________________
Geometry
Ch. 6.1: Angles of Polygons
Now we are going to look at the exterior angles of a polygon and see if we can develop a theorem like we did
for interior angles. To draw the exterior angles, you have to keep your orientation consistent. Start at one vertex
and move either clockwise or counter-clockwise, extending each side as you move along.
Use algebra with a triangle, quadrilateral, pentagon, and hexagon to determine the sum of the exterior angles of
those polygons. Begin by labeling the interior angles with arbitrary letters.
Try to think of how you would justify your hypothesis for any n-gon since we cannot draw all possible cases.
The proof will be in your homework.
Theorem 6.2 – Polygon Exterior Angles Sum: The sum of the exterior angle measures of a convex polygon, one
angle at each vertex, is _________ degrees.