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In the figure above, what is the value of x?
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Jozu
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In the figure above, what is the value of x? [#permalink] New post  Updated on: 20 Jan 2015, 09:36
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In the figure above, what is the value of x?

(A) 55
(B) 60
(C) 65
(D) 70
(E) 75
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Originally posted by Jozu on 18 Jun 2009, 02:27.
Last edited by Bunuel on 20 Jan 2015, 09:36, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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tkarthi4u
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Re: In the figure above, what is the value of x? [#permalink] New post  18 Jun 2009, 03:38
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From the Right angle triangle whose sides are 4 and 3 then Hypotense = 5

Form the Right angle triangle whose one side is 12 and hypotense is 13 then side = 5


So clearly the two side are equal making it into an isosceles triangle .

So 55 + 55 + x = 180

x = 70

Ans . D
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meliha
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Re: In the figure above, what is the value of x? [#permalink] New post  13 May 2011, 19:07
Please excuse me for this ridiculously stupid question, but how do you know that it's:
55 + 55 + x = 180
and not:
55 + 2x = 180

(meaning: how do you know it's not the other 2 angles (the x and unmarked angle) that are the 2 identical angles?)

Thanks
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Re: In the figure above, what is the value of x? [#permalink] New post  13 May 2011, 19:21
one side = 5

other side = 5

So x = (180 - 110) = 70

Answer - D

@meliha, sides opposite to equal angles are equal, so they are equal (opposite to 55 degrees angle), but we don't know yet about x, so we can't assume x is equal to another angle.
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meliha
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Re: In the figure above, what is the value of x? [#permalink] New post  14 May 2011, 07:10
Looked up properties of isoceles triangle last night (after posting my question) and discovered answer to my own question. My understanding is that side the left and right sides are equal (both = 5), then that means the left and right bottom angles are also equal (property of isoc tri), which means that there must be 2 55 deg angles (instead of 2 other sized angles + 55.

55 + 55 + x = 180
x = 180 - 110
x = 70

Got it now, thanks.

Soooo many equations and formulas to memorize/remember... :?
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Re: In the figure above, what is the value of x? [#permalink] New post  20 Jan 2015, 12:24
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In this question,
there are two "Pythagoras triplets" involved.
3-4-5 and 5-12-13
Looking at the dimensions of two right triangles, we can conclude that both the arms of angle "x" are of 5 units of length!

Thus it is an isoseles triangle. So other angle is same as 55 degrees
Thus, x = 180-55-55 = 70 degrees!
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Re: In the figure above, what is the value of x? [#permalink] New post  20 Jan 2015, 19:34
Attachment:
untitled.JPG
untitled.JPG [ 7.64 KiB | Viewed 12007 times ]


The shaded triangle is an isosceles triangles because

both sides are calculated 5 per Pythagoras theorem

Both angles must be same = 55

x = 180 - 2*55 = 70

Answer = D
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Re: In the figure above, what is the value of x? [#permalink] New post  20 Nov 2017, 11:23
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Jozu wrote:
Attachment:
untitled.JPG
In the figure above, what is the value of x?

(A) 55
(B) 60
(C) 65
(D) 70
(E) 75


We see that the right triangle on the left is a 3-4-5 right triangle, and the right triangle on the right is a 5-12-13 right triangle. Thus, the middle triangle has two sides equal to 5. Since one of those sides is opposite a 55-degree angle, the other side must also be opposite a 55-degree angle. Thus, x is:

180 - (55 + 55) = 70.

Answer: D
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