Download Interior Angles of a Polygon_solutions.jnt

Algebra & Analytic Geometry
Interior Angles of a Polygon
Name & Date
Directions: Complete the following table for each polygon. Draw diagonals from a single vertex until the
polygon is separated into non-overlapping triangles. Based on the patterns observed for the first six
polygons, generalize for an n-gon in the last row. Your goal is to find a formula the will find the sum of the
interior angles for any polygon.
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
*********
N-gon
# of sides
# of angles
# of triangles
Total degrees in
a triangle
Total degrees in
the polygon
1) Find the sum of the interior angles of a nonagon.
2) Find the sum of the interior angles of a decagon.
3) Find the sum of the interior angles of a 16-gon.
Directions: Find the indicated measure for each diagram. Note: The diagrams are not drawn to scale.
4)
5)
b
110
a
20
152
60
70
6)
63
80
7)
8) Find the measures of each angle of a triangle formed by 3 adjacent vertices of a regular (equiangular and
equilateral) pentagon.
9) If ABCDEFGH is a regular octagon, find the measures of the angles in
A
B
H
C
I
G
D
F
E
ABI .
10) In the figure below, ABCDE is a regular pentagon and DEFG is a square.
A) Find mDEF .
B) mEDF .
A
B
E
F
C
D
C) Find mAED .
G
A
B
E
C
D
D) Find mDAF .
A
B
E
F
C
D
G