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Bunuel

In the stop sign shown in the figure above, all sides have equal length and all angles have equal measure. If the figure could be rotated 225° in a clockwise direction, point G would be in the position of point

(A) I
(B) J
(C) K
(D) L
(E) M

Attachment:
2017-10-04_1125_001.png
\(\frac{225}{360} = \frac{5}{8}\), which hit me as I calculated what would be central angles. (I do not tote multiples of 45 around in my head.)

If divided by diagonals, each central angle is 45 degrees. There are 8. And 45 * 5 = 225

(I thought about (225 - half a circle), i.e., (225 - 180) . . . Answer is 45. My small "aha": Two 45s is 90, two more is 180, and one more after that is 225. Total of 5.)

G will rotate \(\frac{5}{8}\) of the way around the octagon's center.

Count, clockwise, 5 vertices from G (not inclusive of G). That is L.

Answer D
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Just a thought...is it really necessary to calculate? It's obvious that the line connecting G and K is 180; so rotating 225 would mean that point G will be at the position behind point K which is point L.

Answer is D.
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Paulli1982
Just a thought...is it really necessary to calculate? It's obvious that the line connecting G and K is 180; so rotating 225 would mean that point G will be at the position behind point K which is point L.

Answer is D.

True : G to K is 180 and 225 will be at 45 from K that is at L. But for this you have to calculate angle between K and L which is 45 degrees. And that is what we are calculating here.
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Paulli1982
Just a thought...is it really necessary to calculate? It's obvious that the line connecting G and K is 180; so rotating 225 would mean that point G will be at the position behind point K which is point L.

Answer is D.

True : G to K is 180 and 225 will be at 45 from K that is at L. But for this you have to calculate angle between K and L which is 45 degrees. And that is what we are calculating here.

Thank you Nikkb.


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Bunuel

In the stop sign shown in the figure above, all sides have equal length and all angles have equal measure. If the figure could be rotated 225° in a clockwise direction, point G would be in the position of point

(A) I
(B) J
(C) K
(D) L
(E) M

Attachment:
2017-10-04_1125_001.png

Since the sign has 8 equal sides and 8 equal angles, each rotation from one letter to the next moves the sign 360/8 = 45 degrees.

Thus, if point G is moved 225 degrees, it moves 225/45 = 5 positions going clockwise, so point G would end up at point L.

Answer: D
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Bunuel

In the stop sign shown in the figure above, all sides have equal length and all angles have equal measure. If the figure could be rotated 225° in a clockwise direction, point G would be in the position of point

(A) I
(B) J
(C) K
(D) L
(E) M

Attachment:
2017-10-04_1125_001.png

Since the sign has 8 equal sides and 8 equal angles, each rotation from one letter to the next moves the sign 360/8 = 45 degrees.

Thus, if point G is moved 225 degrees, it moves 225/45 = 5 positions going clockwise, so point G would end up at point L.

Answer: D

Isn't this a octagon with each interior angle as 135 degrees. I didn't get the concept of diving 360 / 8 as for any polygon 360 degrees is the sum of all exterior angles. Experts please explain.
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