Geometry
Notes
Name_________________________
Classifying Polygons
A ____________________ is a closed plane figure with the following properties:
– it is formed by three or more segments called sides
– each side intersects with exactly two sides, one at each endpoint
convex
concave
Classifying Polygons
N
Number of sides
3
4
5
6
7
8
9
10
12
n
T
Type of Polygon
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
dodecagon
n-gon
Vocabulary
Equilateral –
Equiangular –
Regular –
Example 1
Sketch an example of a convex heptagon. Then sketch an example of a concave heptagon.
Finding Angle Measures in Polygons
diagonal –
2
3
Theorem –
The sum of the measures of the interior angles
of a convex n-gon is ______________.
1
4
6
NOT IN VIDEO WILL DO IN CLASS
Number of Sides
Number of Triangles
3
4
5
6
n
5
n=6
Sum of Angles
Corollary –
The sum of the measures of the interior angles of a quadrilateral is 360°.
Examples
1. Find the sum of the measures of the interior angles of a convex octagon.
2. The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon
by the number of sides.
3. A coin is in the shape of a regular 11-gon. Find the sum of the measures of the interior angles.
4. The sum of the measures of the interior angles of a convex polygon is 1440°. Classify the polygon
by the number of sides.
Q
5. Use the diagram to find  S and  T.
156
P 93
85
T
S
6. The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the
measure of the fourth interior angle.
Theorem –
The sum of the measure of the EXTERIOR angles of a convex polygon is ALWAYS 360°.
7. What is the value of x in the diagram?
89
67
2x
x
8. A convex hexagon has exterior angles with measures 34°, 49°, 58°, 67°, and 75°. What is the
measure of an exterior angle at the sixth vertex?
9. Find the measures of an interior angle and an exterior angle of a regular pentagon.
10. Each interior angle of a regular n-gon has a measure of 168°. Find the value of n.
R