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:
- The sum of the exterior angles of any polygon is always 360 degrees
- 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.
- Exteriorangles- are the angles outside of a polygon. Exterior means outside (think exit)
- An exterior angle is an angle between the any side of a shape and a line extended from the next side
- 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
- The sum of the interior angles of a polygon depends on the number of sides
- 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
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.
Step 3:Solve for the missing angle / 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
X = 60
Practice
Find the sum of the interior and exterior angles of each polygon
Polygon name / Number of sides / Sum of interior angles / Sum of exterior angles
1. Quadrilateral / 4 / (4 – 2) 180
(2)180
360 / 360
2. Hexagon / 6 / (6-2)180
(4)180
720 / 360
3. Heptagon / 7 / (7-2)180
(5)180
900 / 360
4. Dodecagon / 12 / (12-2)180
(10)180
1800 / 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
- (4 – 2)180
2(180)
360 - Set the sum you find equal to all of the given angles added together
- Solve for x
- 360 = 60 + 115 + 105 + x
360 = 280 + x
-280 -280
80 = x