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A certain game board is in the shape of a non-convex polygon, with spokes that extend from each vertex to the center of

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by BTGmoderatorDC » Mon May 25, 2020 6:31 pm

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A certain game board is in the shape of a non-convex polygon, with spokes that extend from each vertex to the center of the board. If each spoke is 8 inches long, and spokes are used nowhere else on the board, what is the sum of the interior angles of the polygon?

(1) The sum of the exterior angles of the polygon is 360º.

(2) The sum of the exterior angles is equal to five times the total length of all of the spokes used.


OA B

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Re: A certain game board is in the shape of a non-convex polygon, with spokes that extend from each vertex to the center

by swerve » Tue May 26, 2020 4:09 pm
BTGmoderatorDC wrote: ↑
Mon May 25, 2020 6:31 pm
 A certain game board is in the shape of a non-convex polygon, with spokes that extend from each vertex to the center of the board. If each spoke is 8 inches long, and spokes are used nowhere else on the board, what is the sum of the interior angles of the polygon?

(1) The sum of the exterior angles of the polygon is 360º.

(2) The sum of the exterior angles is equal to five times the total length of all of the spokes used.


OA B

Source: Manhattan Prep
The formula for the sum of the interior angles of a non-convex polygon is (n - 2)(180), where n represents the number of sides. So, from 2 we have

\(360 = 5\cdot 8 \cdot x\)
\(360 = 40x\)
\(9 = x\)

The game board has nine sides. The sum of its interior angles is (9 - 2)(180) = 1260.

Therefore, B
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