SOLUTION: Pleaaaaaaase help me! 5. How many diagonals can be drawn from each vertex of a decagon? 6. How many distinct diagonals does a hexagon have? 7. Calculate the sum of the

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Pleaaaaaaase help me! 5. How many diagonals can be drawn from each vertex of a decagon? 6. How many distinct diagonals does a hexagon have? 7. Calculate the sum of the       Log On

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Question 148644: Pleaaaaaaase help me!

5. How many diagonals can be drawn from each vertex of a decagon?
6. How many distinct diagonals does a hexagon have?
7. Calculate the sum of the interior angles of a convex hexagon.
8. Calculate the sum of the interior angles of a convex 40-gon.
9. If possible, give the name of the convex polygon in which the sum of the interior angles equals 1260°.

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
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%28n-3%29%2F2. In a hexagon (a 6-sided polygon), n = 6, so...
d+=+6%286-3%29%2F2
d+=+9
7) The sum of the interior angles of a polygon is:
S+=+%28n-2%29180degrees. In a hexagon, n = 6, so...
S+=+%286-2%29180%29
S+=+4%28180%29
S+=+720 degrees.
8) The sum of the interior angles of a 40-gon is:
S+=+%2840-2%29180
S+=+38%28180%29
S+=+6840degrees.
9) The sum of the interior angles is:
S+=+%28n-2%29180 and this is given as 1260 degrees, so...
1260+=+%28n-2%29180 Divide both sides by 180.
7+=+n-2 Add 2 to both sides.
n+=+9 This is a nonagon.