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The figure above shown [#permalink] New post 17 Feb 2017, 03:05
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Question Stats:

89% (00:52) correct 10% (00:31) wrong based on 29 sessions


Attachment:
#Grepracticequestion The figure above shows a regular 9-sides polygon.jpg
#Grepracticequestion The figure above shows a regular 9-sides polygon.jpg [ 7.79 KiB | Viewed 2651 times ]


The figure above shows a regular 9-sides polygon. What is the value of X ?

Insert the value

[Reveal] Spoiler: OA
40

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Re: The figure above shown [#permalink] New post 17 Feb 2017, 20:09
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i think answer 15 is wrong. I found an answer 40
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Re: The figure above shown [#permalink] New post 18 Feb 2017, 00:45
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Thank you to point out. I had a mismatch posting the question. :-D

yes, it is true. It is 40. Thank you once again.

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Re: The figure above shown [#permalink] New post 25 Feb 2017, 17:45
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Explanation

The sum of the interior angles of a polygon, use 180(n − 2), where n is the number of sides: Sum of the interior angles = 180(9 − 2) → 180(7) → 1260°.

Since this 9-sided figure is regular, all of the interior angles are equal: 1260° \(\div\) 9 = 140°.

Now we can find x:

Image

x° + 140° = 180°

x = 40°


Hence the value 40 is correct.
[Reveal] Spoiler: Img
Attachment:
di new.jpg
di new.jpg [ 39.94 KiB | Viewed 14840 times ]

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Re: The figure above shown [#permalink] New post 22 Sep 2017, 15:25
isnt 360/n a simpler solution? 360/9=40
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Re: The figure above shown [#permalink] New post 29 Sep 2017, 05:11
saumya17lc wrote:
isnt 360/n a simpler solution? 360/9=40


What's the theory behind your solution?
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Re: The figure above shown [#permalink] New post 29 Sep 2017, 06:48
saumya17lc wrote:
isnt 360/n a simpler solution? 360/9=40


Points to remember:-

Sum of Interior Angles = (n-2) × 180° (n = number of sides)

Each Angle (of a Regular Polygon) = \(\frac{(n-2) * 180}{n}\)
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Re: The figure above shown [#permalink] New post 02 Oct 2017, 07:43
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Attached is a visual that should help.
Attachments

Screen Shot 2017-10-02 at 8.42.42 AM.png
Screen Shot 2017-10-02 at 8.42.42 AM.png [ 126.25 KiB | Viewed 9439 times ]


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Re: The figure above shown [#permalink] New post 28 Mar 2019, 15:10
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Carcass wrote:


Attachment:
#Grepracticequestion The figure above shows a regular 9-sides polygon.jpg


The figure above shows a regular 9-sides polygon. What is the value of X ?

Insert the value

[Reveal] Spoiler: OA
40


Useful rule: the sum of the angles in an n-sided polygon = (n - 2)(180°)

So, the sum of the angles in an 9-sided polygon = (9 - 2)(180°) = 1260°

Since we have a REGULAR 9-sides polygon, each interior angle is EQUAL
1260°/9 = 140°
So, each interior angle is 140°


We get:
Image


Since one of the 140° lies on the same line as angle x we know that the two angles add to 180°
Image
We get" x° + 140° = 180°
Solve: x = 40°

Answer: 40

Cheers,
Brent
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Re: The figure above shown   [#permalink] 28 Mar 2019, 15:10
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