Question

You need to construct a regular polygon. When you draw two sides, the interior angle created between them is 144°,



What will be the sum, in degrees, of the measures of the interior angles of this polygon when it is completed?
Answer







720°








900°








1080°








1440°

Answer 1

the inner sum of angles is 180(n-2) (n number of angles)
so if 180(n-2)=144, then n=10
so 144*10=1440

Answer 2

Another way to figure out without memorizing formulas is to know that the angle formed at the center of the shape is 180-144 = 36. Because there must be 360 degrees at the center, it must therefore be true that the shape has 360/36 = 10 sides.