Carcass wrote:
The diagonal of a polygon is a line segment from any vertex to any non-adjacent vertex. The diagram below shows a regular decagon, a 10-sided polygon, with two diagonals drawn. How many possible diagonals does the regular decagon have?
Attachment:
GRE exam - The diagonal of a polygon is a line segment from any vertex .jpg
A polygon with 10 sides will also have 10 vertices,
Each individual vertex can have 7 diagonals. Here's why:
First, the vertex cannot create a diagonal when connected to itself.
Second, the vertex cannot create a diagonal with the two points on either side of it, since that line will not be a diagonal.
So, in a polygon with 10 vertices, each vertex will have 7 diagonals connected to it.
So, the total number of diagonals = (10)(7) =
70IMPORTANT: Did you see that we counted every diagonal TWICE?
For example, if the line joining vertex A and vertex F is a diagonal, we count that diagonal once when counting the 7 diagonals at vertex A,
AND we count that diagonal once when counting the 7 diagonals at vertex F.
To account for this duplication, we'll divide the number of diagonal by 2.
So, the
TOTAL number of diagonals = 70/2 = 35Answer: 35
Cheers,
Brent