document.write( "Question 148644: Pleaaaaaaase help me! \r
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\n" ); document.write( "\n" ); document.write( "5. How many diagonals can be drawn from each vertex of a decagon?\r
\n" ); document.write( "\n" ); document.write( "6. How many distinct diagonals does a hexagon have?\r
\n" ); document.write( "\n" ); document.write( "7. Calculate the sum of the interior angles of a convex hexagon.\r
\n" ); document.write( "\n" ); document.write( "8. Calculate the sum of the interior angles of a convex 40-gon.\r
\n" ); document.write( "\n" ); document.write( "9. If possible, give the name of the convex polygon in which the sum of the interior angles equals 1260°.\r
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Algebra.Com's Answer #109002 by Earlsdon(6294)\"\" \"About 
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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
\n" ); document.write( "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...
\n" ); document.write( "\"d+=+6%286-3%29%2F2\"
\n" ); document.write( "\"d+=+9\"
\n" ); document.write( "7) The sum of the interior angles of a polygon is:
\n" ); document.write( "\"S+=+%28n-2%29180\"degrees. In a hexagon, n = 6, so...
\n" ); document.write( "\"S+=+%286-2%29180%29\"
\n" ); document.write( "\"S+=+4%28180%29\"
\n" ); document.write( "\"S+=+720\" degrees.
\n" ); document.write( "8) The sum of the interior angles of a 40-gon is:
\n" ); document.write( "\"S+=+%2840-2%29180\"
\n" ); document.write( "\"S+=+38%28180%29\"
\n" ); document.write( "\"S+=+6840\"degrees.
\n" ); document.write( "9) The sum of the interior angles is:
\n" ); document.write( "\"S+=+%28n-2%29180\" and this is given as 1260 degrees, so...
\n" ); document.write( "\"1260+=+%28n-2%29180\" Divide both sides by 180.
\n" ); document.write( "\"7+=+n-2\" Add 2 to both sides.
\n" ); document.write( "\"n+=+9\" This is a nonagon.
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