Transcript Sum of Interior Angles and Number of Diagonals in a Polygon

Angles and Diagonals in
Polygons
The interior angles are the angles
inside the polygon.
The sum of the
interior angles is
found when you
add up all the
angles inside a
polygon.
On a separate piece of paper:
Fill in the rest of the table:
Shape
Triangle
Number
of Sides
Sum of
Interior
Angles
3
0
Quadrilateral
360
Pentagon
540
Hexagon
6
720
Heptagon
7
900
Octagon
Number of
Diagonals
5
14
1) What are the patterns that you notice
in the sum of interior angles?
2) What are the patterns that you notice
in the number of diagonals?
Formula to find Sum of Interior Angles
Sum = 180(n – 2), when n is the number
of sides.
For example: Triangle = 3 sides
= 180(n – 2)
= 180(3 – 2)
= 180(1)
= 180
Formula to find the number of
diagonals in a polygon:
When n = number of sides in the polygon
n(n  3)
diagonals 
2
For example in a hexagon:
6(6  3) 6(3) 18



9
2
2
2
On the same paper as before,
answer the following:
1) What is the sum of interior angles of a polygon
with ten sides?
2) What is the sum of interior angles of a polygon
with fifteen sides?
3) What is the sum of interior angles of a polygon
with 20 sides?
4) How many diagonals are in a shape with eleven
sides?
5) How many diagonals are in a shape with
seventeen sides?