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Geometry 8-1 Angles of Polygons
A. Sum of Measures of Interior Angles
1. Interior angles - The sum of
the measures of the angles of
each polygon can be found by
adding the measures of the
angles of a triangle.
2. Theorem 8-1 (Interior
angle sum Theorem)
-If a convex polygon has n
sides and S is the sum of
the measures of the interior
angles, then S = 180(n - 2).
Convex
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
# of
sides
3
4
5
6
7
8
# of
’s
1
2
3
4
5
6
Sum of Angle
Measures
(1 180) or 180
(2 180) or 360
(3 180) or 540
(4 180) or 720
(5 180) or 900
(6 180) or 1080
Ex 1: Find the measure of each interior angle of a regular pentagon.
-Use the interior angle sum theorem to find the sum of the angle measures.
S = 180(n - 2)
S = 180(___- 2)
S = ______
so each angle is ____/5 or ______.
Ex 2: Find the measure of each interior angle.
B. Sum of Measures of Exterior Angles
1. Theorem 8-2 Exterior Angle Sum Theorem - If a polygon is convex, then the
sum of the measures of the exterior angles, one at each vertex is 360.
Ex 3: Find the measures of an exterior and interior angle for a regular hexagon.
HW: Geometry 8-1 p. 407-409
14-32 even, 40, 47-48, 49-55 odd, 59-65 odd