Question 148644
5) The number of diagonals that can be drawn from each vertex of an n-sided polygon (n = 10 in a decagon) is (n-3) = 10-3 = 7
6) The number of distinct diagonals (d) that can be drawn in a polygon of n sides is: {{{d = n(n-3)/2}}}.  In a hexagon (a 6-sided polygon), n = 6, so...
{{{d = 6(6-3)/2}}}
{{{d = 9}}} 
7) The sum of the interior angles of a polygon is:
{{{S = (n-2)180}}}degrees. In a hexagon, n = 6, so...
{{{S = (6-2)180)}}}
{{{S = 4(180)}}}
{{{S = 720}}} degrees.
8) The sum of the interior angles of a 40-gon is:
{{{S = (40-2)180}}}
{{{S = 38(180)}}}
{{{S = 6840}}}degrees.
9) The sum of the interior angles is:
{{{S = (n-2)180}}} and this is given as 1260 degrees, so...
{{{1260 = (n-2)180}}} Divide both sides by 180.
{{{7 = n-2}}} Add 2 to both sides.
{{{n = 9}}} This is a nonagon.