PS - gmatprep - triangle

Question

ps

Ferihere · Answer

1. insufficient, since longer line SU can be any size interms of it may change the proportion.

2. insufficient, now shorter line can be any size and it will impose uncertainty

Together they are suff. since both lines fixed by the means of they have to be one side of isoclese triangles.

x=45
 
Ans: C

domleon · Answer

guys - i just don´t get his explanation ... can someone help me on this?

thanx

tmmyc · Answer

https://www.postimage.org/aV1dLTlr.jpg

1 is insufficient because it only tells us that RSQ is isoceles.
2 is insufficient because it only tells us that TSU is isoceles.

Both together are sufficient because given the two isoceles triangles, we can determine angle x like so:

1)
From line RST
a + x + b = 180

2)
From triangle RPT
y + 90 + z = 180
-> y + z = 90

3)
From triangle RSQ
y + a + a = 180

4)
From triangle STU
z + b + b = 180

Combine 3) and 4) and call it 5)
z + y + 2a + 2b = 360

Combine 5) with 2) and call it 6)
90 + 2a + 2b = 360
-> a + b = 135

Combine 6) with 1) to solve for x
x = 45

PS - gmatprep - triangle

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