If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Class 6>Unit 8

Lesson 3: Angle sum property of polygons

# Sum of interior angles of a polygon

To find the interior angle sum of a polygon, we can use a formula: interior angle sum = (n - 2) x 180°, where n is the number of sides. For example, a pentagon has 5 sides, so its interior angle sum is (5 - 2) x 180° = 3 x 180° = 540°. Created by Sal Khan.

## Want to join the conversation?

• So if we know that a pentagon adds up to 540 degrees, we can figure out how many degrees any sided polygon adds up to. Hexagon has 6, so we take 540+180=720. A heptagon has 7 sides, so we take the hexagon's sum of interior angles and add 180 to it getting us, 720+180=900 degrees. Same thing for an octagon, we take the 900 from before and add another 180, (or another triangle), getting us 1,080 degrees. So we can use this pattern to find the sum of interior angle degrees for even 1,000 sided polygons. Of course it would take forever to do this though. :)
• There is an easier way to calculate this. Use this formula: 180(n-2), 'n' being the number of sides of the polygon. But you are right about the pattern of the sum of the interior angles.
• Whys is it called a polygon? Why not triangle breaker or something?
• polygon breaks down into poly- (many) -gon (angled) from Greek. So a polygon is a many angled figure. Maybe your real question should be why don't we call a triangle a trigon (3 angled), or a quadrilateral a quadrigon (4 angled) like we do pentagon, hexagon, heptagon, octagon, nonagon, and decagon.
• What if you have more than one variable to solve for how do you solve that
• The rule in Algebra is that for an equation(or a set of equations) to be solvable the number of variables must be less than or equal to the number of equations. For example, if there are 4 variables, to find their values we need at least 4 equations. If the number of variables is more than the number of equations and you are asked to find the exact value of the variables in a question(not a ratio or any other relation between the variables), don't waste your time over it and report the question to your professor.
• Sal, can you explain what a rhombidodecadodecahedron?
• Rhombicosidodecahedron

In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.

It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
• a circle is 360 degrees so can I say it is made up of 2 triangles?? But it is hard to visualise...
• A circle is not a polygon. A polygon is a closed figure with at least 3 straight sides. A circle is not considered a polygon because it is a curved shape and does not have sides or angles.
Hope this helps. :)
• Is their a simpler way of finding the interior angles of a polygon without dividing polygons into triangles ?
• well there is a formula for that:
n(no. of sides) - 2 * 180
that will give you the sum of the interior angles of a polygon
• How do you x by multiply y x e =
• Around in the video, how is 2+(s-4) simplified to become s-2?