Class notes: The sum of the Interior and exterior angles of polygons
What is the sum of interior angles of a polygon?
What is the sum of the exterior angles of a polygon?
3 terms you must know: interior angle, external angle and sum
 Today’s key ideas:
1. The sum of the exterior angles of any polygon is always 360 degrees
2. The sum of the interior angles of a polygon depends on the number of sides in a polygon and it
can be found using the formula 180(n-2), where n is the number of sides.
How do you find the Sum?
 The sum is the total amount. You get the sum of angles by adding all angles in a shape together.
 Exterior angles- are the angles outside of a polygon. Exterior means outside (think exit)
o An exterior angle is an angle between the any side of a shape and a line extended from the
next side
o The sum of the exterior angles of any polygon is always 360 degrees

Interior angles- are the angles inside of a polygon. INterior means INside
o The sum of the interior angles of a polygon depends on the number of sides
o The sum of the interior angles of a polygon can be found using the formula 180(n-2),
where “n” is the number of sides of the polygon
 To find the sum of the interior angles of a triangle, we would plug in ___ for n
 To find the sum of the interior angles of a pentagon, we plug in ___ for n
Sample problem 1:
What is the sum of the exterior angles of a triangle/ square/ pentagon/ hexagon/ dodecagon?
A: 360 degrees. The sum of exterior angles is always 360 degrees, no matter what the shape is.
Sample problem 2:
What is the sum of the interior angles of a quadrilateral (4-sided shape)?
To find the sum of interior angles, use the formula:
(n-2)180, where n is the number of sides
(4-2)180
2(180)
360
Step 1: Ask yourself, what is the sum
of the interior angles of any pentagon?
Step 2: Set the sum of all of the given
angles and the missing angle (x) equal
to the sum of the interior angles in a
pentagon.
To find the sum of interior angles, we use the formula
(n-2) 180, where n is the number of sides.
(5-2)180 (since a pentagon has 5 sides)
3(180)
540 is the sum of the angles in a pentagon
155 + 100 + 85 + 140 + x = 540
480 + x = 540
-480
-480
Step 3: Solve for the missing angle
X = 60
Practice
Find the sum of the interior and exterior angles of each polygon
Polygon name
Number of sides
Sum of interior angles
1. Quadrilateral
4
2. Hexagon
6
3. Heptagon
7
4. Dodecagon
12
(4 – 2) 180
(2)180
360
(6-2)180
(4)180
720
(7-2)180
(5)180
900
(12-2)180
(10)180
1800
Sum of exterior
angles
360
360
360
360
5. Find the measure of the missing interior angle of the shape on the board.
 # of sides = 4
Given interior angle measures: 60, 115, 105, x
 Use the interior angle sum formula to find the total number of angles in a polygon
with 4 sides
o (4 – 2)180
2(180)
360
 Set the sum you find equal to all of the given angles added together
 Solve for x
o 360 = 60 + 115 + 105 + x
360 = 280 + x
-280 -280
80 = x