Warm Up
On your Geoboard create a quadrilateral.
Take Note
diagonal
A segment that connects two vertices not next to
each other.
Geoboards
• How many triangles are in a pentagon?
(Don’t cross other rubber bands)
• How many triangles are in a Hexagon?
Take Note
Interior Angle Sum Thm.
Description: The sum of the interior angles of a n-sided
convex polygon is 𝑛 − 2 ∙ 180°
Diagram:
n=5
Example/Name: The sum of this pentagon is 5 − 2 ∙ 180°
𝟓𝟒𝟎°
You Try
A. Find the sum of the measures of the interior
angles of a:
Recall: 𝒏 − 𝟐 ∙ 𝟏𝟖𝟎°
Hexagon 
13-gon 
𝟔 − 𝟐 ∙ 𝟏𝟖𝟎° = 𝟕𝟐𝟎°
𝟏𝟑 − 𝟐 ∙ 𝟏𝟖𝟎° = 𝟏𝟗𝟖𝟎°
Has 13 sides
20-gon 
Has 20 sides
𝟐𝟎 − 𝟐 ∙ 𝟏𝟖𝟎° = 𝟑𝟐𝟒𝟎°
Example 1
Find the Interior Angles Sum of a Polygon
B. Find the measure of each interior angle of
parallelogram RSTU.
Step 1 Add ‘em up.
Step 2 Solve for x.
Step 3 Substitute.
𝒒𝒖𝒂𝒅𝒓𝒊𝒍𝒂𝒕𝒆𝒓𝒂𝒍 𝒉𝒂𝒔 𝟑𝟔𝟎°
You Try
B. Find the value of x.
A. x = 7.8
B. x = 22.2
C. x = 15
D. x = 10
Take Note
Exterior Angle Sum Thm.
Description: The sum of the exterior angles of a n-sided
convex polygon is always 360°
Diagrams:
A. Find the value of x in
the diagram.
A. 72
B. 88
C. 52
D. 60
Let’s Try
B. Find the measure of each exterior angle of a
regular pentagon.
Let’s Try
A. 72
B. 60
C. 45
D. 90
Wrap Up
On a half sheet of paper do the following:
1. What is the interior sum of a heptagon (7-sides)?
2. What is it’s exterior sum?
Homework
HW 40: Pg.397-399 #’s 1-11, 14, 16, 22,
26, 30
Hint: Regular means all the same angles and sides