Sum of interior angles in a polygon = 180 (n-2) where n = number of sides
A ten-sided polygon, obviously, has 10 sides (decagon).
The sum of the interior angles of decagon = 180 (n-2)
= 180 (10-2)
= 180 (8)
= 1,440 degrees
Explanation of the pattern:
It is the expression in finding the number of triangles in a polygon, where n=number of sides. The sum of interior angles of triangle is 180 degrees. Multiply 180 degrees by the number of triangles in a polygon yields the sum of the interior angles of the same polygon.
Decagon has 8 triangles inside it (10 sides - 2). Multiply the number of triangles by 180 degrees, the result is 1,440 degrees.