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In the figure above, what is the value of x? [#permalink]
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Updated on: 20 Jan 2015, 10:36
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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, 03:27.
Last edited by Bunuel on 20 Jan 2015, 10:36, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



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Re: In the figure above, what is the value of x? [#permalink]
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18 Jun 2009, 04:38
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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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Re: In the figure above, what is the value of x? [#permalink]
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13 May 2011, 20:07
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]
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13 May 2011, 20:21
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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Re: In the figure above, what is the value of x? [#permalink]
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14 May 2011, 08:10
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]
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20 Jan 2015, 13:24
In this question, there are two "Pythagoras triplets" involved. 345 and 51213 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 = 1805555 = 70 degrees!



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Re: In the figure above, what is the value of x? [#permalink]
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20 Jan 2015, 20:34
Attachment:
untitled.JPG [ 7.64 KiB  Viewed 4273 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]
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20 Nov 2017, 12:23
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 345 right triangle, and the right triangle on the right is a 51213 right triangle. Thus, the middle triangle has two sides equal to 5. Since one of those sides is opposite a 55degree angle, the other side must also be opposite a 55degree angle. Thus, x is: 180  (55 + 55) = 70. Answer: D
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