Download Chapter 11 – Area of Polygons and Circles Section 11.1

Chapter 11 – Area of Polygons and Circles
Section 11.1 - Angle Measures in Polygons
*Watch this video to give you a better grasp of the concepts listed below.*
Polygon
# of sides
# of
's
Sum of interior angles
Triangle
Quadrilateral
Pentagon
Hexagon
Decagon
n-gon
Theorems about Interior Angles
Thm 11.1- Polygon Interior Angles Thm.
The sum of the measures of the interior angles of a convex n-gon is:
Corollary to Thm 11.1
The measure of each interior angle of a regular n-gon is:
Exterior angle:
Theorems about Exterior Angles
Thm 11.2 - Polygon Exterior Angles Thm
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex,
is 360°.
Corollary to Thm 11.2
The measure of each exterior angle of a regular n-gon is:
Example 1:
A heptagon has 4 interior angles that measure 160° each and 2 interior angles
that are right angles. What is the measure of the other interior angle?
Example 2:
The measure of each interior angle of a regular polygon is 165 . How many sides does the
polygon have?
Example 3:
The sign has a hexagon shape. Four of the interior angles measure 140° and the remaining
angles are congruent. What is the measure of the congruent angles?
Example 4:
Example 5:
The measure of each exterior angle of a regular polygon is 40°. How many sides does the
polygon have?
Example 6:
If you were designing a sign, would it be possible to make a sign that is a regular polygon with
each interior angle measure of:
a) 160°
b) 115°