Xbond wrote:Hi there,

I woud like your input about this difficult geometry question. Someone can explain to me in simple way the concept. Sorry, I don't know the answer. Look at the attachment.

In the figure shown, what is the value of x ?
(1) The length of line segment QR is equal to the length of line segment RS.
(2) The length of line segment ST is equal to the length of line segment TU.

I think the answer is C... both together will give an answer, none individually.
When you use both together, along with the property that the angles opposite to equal sides are equal in a triangle and sum = 180 for a triangle, You will be able to work out the question.

1. Since QR and RS are equal, you can label two of the internal angles of QRS as Y and the third angle as 180 -2y. No more info. Insuff.
2. Since ST and TU are equal, you can label two of the internal angles of STU as z and the third angle as 180 – 2z. No more info. Insuff.
When we combine, our three angles in the larger triangle are 90 + (180 – 2y) + (180 – 2z) = 180.
This works out to z + y = 135
Sine x lies on a straight line, the angle is 180 – 135 = 45
Hope I have this right. C seems too easy so if someone thinks the statements are suff. On their own, let us know.

Hi ,
The answer is definitely C
because here is the simple way to deduce:
Ok lets consider the triangle QRS it has two equal angles ,lets call it S
same the SUT triangle has two equal angles,lets acll it U
then angle T+2U=180
angle R+2S=180
---------------------
adding both T+R+2(S+U)=360
we know T+R+P =180
-------------------------
substracting both 2(S+U)-P=180
2(S+U)-90=180
S+U=270/2=135
and from the figure we know that S+U+X=180
=>X=180-135=45

we used bothe the statement to deduce this ,therefore answer is C

the right answer is C