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## Class 8 Math (Assamese)

### Unit 3: Lesson 2

Angle sum property

# Sum of interior angles of a polygon

Learn how to find the sum of the interior angles of any polygon. 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.
• Is their a simpler way of finding the interior angles of a polygon without dividing polygons into triangles ? • Which angle is bigger: angle a of a square or angle z which is the remaining angle of a triangle with two angle measure of 58deg. and 56deg. ? • why does Sal say that it is a 5 sided polygon when it is a 8 sided? I think please vote • What does he mean when he talks about getting triangles from sides? • Sal is saying that to get 2 triangles we need at least four sides of a polygon as a triangle has 3 sides and in the two triangles, 1 side will be common, which will be the extra line we will have to draw(I encourage you to have a look at the figure in the video). The four sides can act as the remaining two sides each of the two triangles. As we know that the sum of the measure of the angles of a triangle is 180 degrees, we can divide any polygon into triangles to find the sum of the measure of the angles of the polygon. I hope that helps.
• For a polygon with more than four sides, can it have all the same angles, but not all the same side lengths? What are some examples of this?
(1 vote) • Sure. Imagine a regular pentagon, all sides and angles equal. Orient it so that the bottom side is horizontal.

Now remove the bottom side and slide it straight down a little bit. Extend the sides you separated it from until they touch the bottom side again. They'll touch it somewhere in the middle, so cut off the excess.

Now, since the bottom side didn't rotate and the adjacent sides extended straight without rotating, all the angles must be the same as in the original pentagon. That is, all angles are equal. But clearly, the side lengths are different. The bottom is shorter, and the sides next to it are longer.

We can even continue doing this until all five sides are different lengths.
• k but what about exterior angles?  