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# In the stop sign shown in the figure above, all sides have equal lengt

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Math Expert
Joined: 02 Sep 2009
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In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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05 Oct 2017, 01:38
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72% (01:10) correct 28% (01:33) wrong based on 46 sessions

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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

[Reveal] Spoiler:
Attachment:

2017-10-04_1125_001.png [ 7.07 KiB | Viewed 588 times ]
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132595 [0], given: 12326

Senior Manager
Joined: 02 Jul 2017
Posts: 269

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Location: India
Re: In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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05 Oct 2017, 02:48
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KUDOS
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

=> Given figure is a regular Octagon ( All sides and angles are equal)
=> All the angles at center point O will be equal= 360/8 = 45
=> Angles GOH = HOI = IOJ = ..... = 45 degree

So When the figure is rotated Clockwise by 225 => Point G will move 225 degrees
=> 225/45 = 5 sections => G-> H = 45 degree => G -> I 90 degree . ..... So for 225 G will reach L

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Intern
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Re: In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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05 Oct 2017, 04:30
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---
Here you have first find out degrees of every angle . then, divide the 225 with this degrees of each angle.

=> Given figure is a regular Octagon ( All sides and angles are equal)
=> All the angles at center point O will be equal= 360/8 = 45
=> Angles GOH = HOI = IOJ = ..... = 45 degree

So When the figure is rotated Clockwise by 225 => Point G will move 225 degrees
=> 225/45 = 5 sections => G-> H = 45 degree => G -> I 90 degree . ..... So for 225 G will reach L

Kudos [?]: 7 [0], given: 182

Director
Joined: 22 May 2016
Posts: 977

Kudos [?]: 336 [0], given: 591

In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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06 Oct 2017, 21:44
Bunuel wrote:

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

[Reveal] Spoiler:
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.

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Intern
Joined: 29 May 2012
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Re: In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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06 Oct 2017, 22:51
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.

Kudos [?]: 4 [0], given: 11

Senior Manager
Joined: 02 Jul 2017
Posts: 269

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Location: India
Re: In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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06 Oct 2017, 23:06
Paulli1982 wrote:
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.

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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Intern
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Re: In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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06 Oct 2017, 23:09
Nikkb wrote:
Paulli1982 wrote:
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.

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.

Sent from my iPhone using GMAT Club Forum mobile app

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Target Test Prep Representative
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Re: In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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09 Oct 2017, 16:45
Bunuel wrote:

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

[Reveal] Spoiler:
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.

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Re: In the stop sign shown in the figure above, all sides have equal lengt [#permalink]

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10 Oct 2017, 03:28
ScottTargetTestPrep wrote:
Bunuel wrote:

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

[Reveal] Spoiler:
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.

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.

Kudos [?]: 3 [0], given: 2

Re: In the stop sign shown in the figure above, all sides have equal lengt   [#permalink] 10 Oct 2017, 03:28
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