Question
Arun draws a regular 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 360∘.
(2) The sum of the exterior angles is equal to five times the total length of all of the spokes used.
(1) The sum of the exterior angles of the polygon is 360∘.
(2) The sum of the exterior angles is equal to five times the total length of all of the spokes used.
Answer: Option A
:
A
The sum of the exterior angles of any polygon is 360∘. Hence, statement is of no use to us
From statement 2-
The sum of the exterior angles = 5 × length of each spoke × number of spokes.
360 = 5(8)(x)
360 = 40x
9 = x
The game board has nine sides. The sum of its interior angles is (9 - 2)(180) = 1260. Statement 2 alone is sufficient
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:
A
The sum of the exterior angles of any polygon is 360∘. Hence, statement is of no use to us
From statement 2-
The sum of the exterior angles = 5 × length of each spoke × number of spokes.
360 = 5(8)(x)
360 = 40x
9 = x
The game board has nine sides. The sum of its interior angles is (9 - 2)(180) = 1260. Statement 2 alone is sufficient
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