In the figure shown, what is the value of x?

[Ladan]

Hi,

I don't understand how x can be solved with the given information. The correct answer is C. Please advise. Thanks!

[GMAT 2007]

Ladan,

In quad. PQSU, if we know Angle(SQP) (assume a) and Angle(SUP) (assume b) or if we know their sum then X can be calculated, because

we know 90 + a + b + x = 360...(1)

from statement (1) we know Angle RQS = Angle RSQ ( QR=RS) and Angle(RSQ) = 180 -a
from statemtn (2) we know Angle SUT = Angle TSU (ST = UT) and Angle(TSU) = 180 -b

Since RT is a straight line, we know x + 180-a + 180 -b = 180 or x -(a+b) = -180 or (a+b) = x + 180

If you substitute the the value of a+b in (1) X can be calculated.

Hope it helps

GMAT 2007