what will be sum of measures of a conven polygon with 15 sides.
Answers
Step-by-step explanation:
1440 Degrees
There are two formulas/methods for finding the sum of the interior angles of a convex polygon.
Method #1)
You can divide a convex polygon into non-overlapping triangles by drawing all the diagonals of the polygon from a single point. When you do this you will get two less triangles than the number of sides. So a 10 sided convex polygon (decagon) will have 8 triangles. Since each triangle has an angle sum of 180 degrees 8 triangles will have an angle sum of 8 X 180 = 1440 degrees.
So this uses the formula (n-2)(180).

Method #2 ) The sum of the exterior angles of any convex polygon is 360 degrees. The sum of each pair of exterior and interior angles is 180 degrees (Supplementary pairs). This means you have 10 supplementary pairs. 10 X 180 - 360 (for the sum of the exterior angles). 10 X 180 = 1800. 1800 - 360 = 1440 degrees.

So this method uses the formula (n X 180) - 360. Which is algebraically the same as (n-2)(180).