can the following formula to find the sum of the interior angles of a polygon be used on a concave polygon?
180(n-2)
where n= the number of sides
Does anyone have the full geometry b semester exam
Sorry, it's 180(n-2), because each triangle adds up to 180 degrees, minus the central angles at a point.
I am confused, is the formula
360(n-2), or 180(n-2)?
Yes.
You can prove it as follows:
From any point inside of the polygon that can connect directly to all the vertices (i.e. without crossing any side of the polygon), connect to all the vertices to form n triangles.
The sum of the interior of the n triangles is n*180. From this we subtract the angles at the point (360°) which do not form part of the interior angles. Thus the sum of the interior angles of a polygon, concave or convex, regular or not regular, is 360(n-2)°.