Polygonal Angles 5 – General Formula for Vertex Angle

To know this, one must know the formula for working out the combined interior angles. This is 180 multiplied by 2 less than the number of sides. i.e. 108(n-2). This is because we can imagine splitting a polygon into (n-2) triangles from one vertex. There are 180 degrees in a triangle and thus we multiply the number of triangles formed in the polygon by 180. To find the size of the angle at each individual vertex, divide by the number of sides. This means we get [180(n-2)]/n

Or alternatively, to find the size of each angle in radians, we would use [π(n-2)]/n. This is because 180 degrees is known at π radians, and there are therefore π radians in a triangle.

formula for polygon angles vertex sum is 180(n-2).So to find out vertex angle alone it is 180(n-2)/n K.K.GARG,India

correct answer is 180(n-2)/n

As we know that the sum of all angles of polygon is 180(n-2), where n is the total no. of vertices. Now dividing the sum of all angles by total no. of vertices i.e. (180(n-2))/n is the required answer. In this problem the total no. of vertices are n=12, and the sum of all angles is 180(12 - 2)=1800. Now dividing the 1800/12 = 150 is our required answer.

to find the sum of interior angles we use 180(n-2).to find the vertex angle it should be divide by n. therefore the correct answer is 180(n-2)/n