Geometry – Chapter 10 Lesson Plans
Section 10.2 – Diagonals and Angle Measurements
Enduring Understandings: The student shall be able to:
1. Find measures of interior and exterior angles of polygons.
Standards:
14. Points, Lines and Planes
States and applies the triangle sum, exterior angles, and polygon angle sum theorems.
Essential Questions: How can we calculate the internal and external angles of polygons?
Activities:
1. Talk about what internal angles are.
 Internal angles are “inside” the polygon between two consecutive sides.
 How do you know the interior angles of a triangle add to 180? Do the proof using
parallel lines knowing alternate interior angles of a transversal between parallel lines
are equal:

The measure of the interior angles (in degrees) of a triangle is 180.
2. What are the sum of the measures of the interior angles of an n-gon? Develop it by
making a table and looking for the pattern:
Polygon
Triangle
Quadrilateral
Pentgagon
Hexagon

n-gon
Number of Sides (n)
3
4
5
6

n
Number of
Triangles
1
2
3
4

n-2
Sum of measures of
interior angles
1 * 180 = 180
2 * 180 = 360
3 * 180 = 540
4 * 180 = 720

(n-2) * 180
Thm 10-1: The measure of the total interior angles (in degrees) of an n-gon is (n2)*180, where n is the number of sides.
The measure of each interior angle of a regular n-gon is: (n-2)*180/n

Examples
o What is the measure of the internal angles of a 12 sided polygon? (12-2)*180
= 1800
o If there are 1440 internal degrees to a polygon, how many sides does it have?
(n-2)*180=1440, so n = 10 sides
o The measure of each interior angle of a regular polygon is 140. How many
sides does the polygon have? (n-2)*180/n = 140, n = 9
3. Talk about what external angles are.
 External angles are “outside” the polygon, measured from an extended side to the
next side.
Exterior angles

Does it matter which side we extend? No – we will get the same answer.
4. What is the measure of the exterior angles of a polygon?
 Activity: Have three come up and each hold a point in a length of yarn. Teacher
explains the measure of the external angles of a polygon is from the direction on one
side of the polygon to the direction of the next leg or side. Can be thought of as
walking around the polygon. Walk around the triangle and talk about each angle, and
when you get back to the starting point you went one revolution. How many degrees
in one revolution? 360.
 Do the above again with four students and then five. Still one revolution to go all the
way around, or 360.
 Thm 10-2: The measure of the external angles of an n-gon is 360.
 Examples
o What is the measure of the external angles of a 7 sided polygon? 360
o What is the measure if each external angle if a 6 sided regular polygon? 60
Lesson/Body:
Assessments:
Do the “Check for Understanding”
Interior Angles
Total Measure
(all concave polygons)
(n – 2) * 180
Exterior Angles
360
CW WS 10.2 of the Blue book, or 10.1 of the Red Book
HW pg 411-412, # 9 - 25 odd (9)
Measure of Each
(Regular Polygon)
(n  2) * (180)
n
360
n