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# The hexagon above has interior angles whose measures are all equal. As

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Math Expert
Joined: 02 Sep 2009
Posts: 54544
The hexagon above has interior angles whose measures are all equal. As  [#permalink]

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28 Jul 2017, 02:05
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:53) correct 42% (02:02) wrong based on 52 sessions

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The hexagon above has interior angles whose measures are all equal. As shown, only five of the six side lengths are known: 10, 15, 4, 18, and 7. What is the unknown side length?

(A) 7

(B)10

(C) 12

(D) 15

(E) 16

Attachment:

Hexagon_1.jpg [ 12.03 KiB | Viewed 1763 times ]

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Re: The hexagon above has interior angles whose measures are all equal. As  [#permalink]

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28 Jul 2017, 05:09
1
Bunuel wrote:

The hexagon above has interior angles whose measures are all equal. As shown, only five of the six side lengths are known: 10, 15, 4, 18, and 7. What is the unknown side length?

(A) 7

(B)10

(C) 12

(D) 15

(E) 16

Attachment:
Hexagon_1.jpg

No formula/logic coming to my mind
I f i had to guess i will go with C (12)
10 + 15 = 18 + 7
if we put 12 in place
then
10+12 = 18 + 4
Also 7 + 12 = 4 + 15

Some sort of number logic coming out which is maintaining a symmetry (All internal angles are same)
So yes C (Move on)
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Luckisnoexcuse
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Joined: 02 Aug 2009
Posts: 7589
The hexagon above has interior angles whose measures are all equal. As  [#permalink]

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28 Jul 2017, 05:34
2
2
Bunuel wrote:

The hexagon above has interior angles whose measures are all equal. As shown, only five of the six side lengths are known: 10, 15, 4, 18, and 7. What is the unknown side length?

(A) 7

(B)10

(C) 12

(D) 15

(E) 16

Attachment:
The attachment Hexagon_1.jpg is no longer available

hi..
Pretty tough for anyone not very good at geometry to be not above 700
pl see att fig..
join the lines to make a equilateral triangle..
all three vertices of bigger triangle will form 3 equilateral triangle as exterior angle = 180-120=60

so the three sides of bigger triangle will be equal ..
10+15+4=10+?+7....?=29-17=12
C
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Re: The hexagon above has interior angles whose measures are all equal. As  [#permalink]

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28 Jul 2017, 07:29
1
chetan2u wrote:
Bunuel wrote:

The hexagon above has interior angles whose measures are all equal. As shown, only five of the six side lengths are known: 10, 15, 4, 18, and 7. What is the unknown side length?

(A) 7

(B)10

(C) 12

(D) 15

(E) 16

Attachment:
Hexagon_1.jpg

hi..
Pretty tough for anyone not very good at geometry to be not above 700
pl see att fig..
join the lines to make a equilateral triangle..
all three vertices of bigger triangle will form 3 equilateral triangle as exterior angle = 180-120=60

so the three sides of bigger triangle will be equal ..
10+15+4=10+?+7....?=29-17=12
C

Hello Sir,

Is there any other way to solve this? This one seems tough in which we have to construct a triangle from a given hexagon!
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Math Expert
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Posts: 7589
Re: The hexagon above has interior angles whose measures are all equal. As  [#permalink]

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28 Jul 2017, 09:36
pikolo2510 wrote:
chetan2u wrote:
Bunuel wrote:

The hexagon above has interior angles whose measures are all equal. As shown, only five of the six side lengths are known: 10, 15, 4, 18, and 7. What is the unknown side length?

(A) 7

(B)10

(C) 12

(D) 15

(E) 16

Attachment:
Hexagon_1.jpg

hi..
Pretty tough for anyone not very good at geometry to be not above 700
pl see att fig..
join the lines to make a equilateral triangle..
all three vertices of bigger triangle will form 3 equilateral triangle as exterior angle = 180-120=60

so the three sides of bigger triangle will be equal ..
10+15+4=10+?+7....?=29-17=12
C

Hello Sir,

Is there any other way to solve this? This one seems tough in which we have to construct a triangle from a given hexagon!

Hi,

it will be important to draw a triangle here..
May be slightly easier if you understand that the OPPOSITE sides will be parallel and the distance between these sides will be same because of the 120 degree angle
this basically means..
1) PARALLEL sides 10 and 18..
sides in between $$15+4=?+7......?=19-7=12$$
2) PARALLEL sides 15 and 7..
$$4+18=?+10...?=22-10=12$$

and this comes from the fact that the exterior angle are 180-120 = 60 making equilateral angles..

other way would be to may be guess from the proportional lenggth as it is not given that the diagram is not as per scale..
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Re: The hexagon above has interior angles whose measures are all equal. As   [#permalink] 28 Jul 2017, 09:36
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