Why 180(n 2)

It is a bit difficult but I think you are smart enough to master it. Let x n be the sum of interior angles of a n-sided polygon. So you may say that x n-1 is the sum of interior angles of an n-1 -sided polygon. As in the diagram, if you cut away one vertex, say A 1 , of an n-sided polygon you can get an n-1 sided polygon, A 2 A 3 A 4 …A n.

So, you get the difference equation:. Lastly, we get the angle sum of triangle. Adding up all the n-2 equalities, and canceling all the terms, we get. Insight Wow! We find that the sum is degrees. This is an important fact to remember. To find the sum of the interior angles of a quadrilateral, we can use the formula again. This time, substitute 4 for n. We find that the sum of the interior angles of a quadrilateral is degrees. Polygons can be separated into triangles by drawing all the diagonals that can be drawn from one single vertex.

Let's try it with the quadrilateral shown here. From vertex A, we can draw only one diagonal, to vertex D. Joffan Joffan Would you care to explain. So we're not "inside" or "outside" the polygon, we're just using different labels to describe different aspects of the angle at the vertex.

Choose an edge on the triangle and mark a point on it. Now imagine pulling the point outwardly away from the edge. Karl Karl 4, 4 4 gold badges 15 15 silver badges 23 23 bronze badges. Travis Willse Travis Willse Isha Tarte Isha Tarte 1 1 silver badge 6 6 bronze badges.

Sign up or log in Sign up using Google. Sign up using Facebook. It's true that it's confusing. If you're drawing the triangles all coming from the center, the thing to realize is that the n-2 isn't because there are n-2 triangles.

There are clearly n triangles when you draw it out that way. Instead, the -2 comes out of the math. Let's consider what happens when you draw these triangles. They all come out from one point in the center, n in total.