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

[wishmeluck]

Official Answer to this problem is (C). Can someone please help me with an explanation? I think you have to use similar triangles to do this, but have no idea as to how.

Thanks very much in advance!
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[tato4ka]

1) < QSR = < SRQ = Y and <UST = <SUT = Z
2) X = 180 - Y - Z (cos those angles are one the same line)
3) X = 360 - (180 - Y) - (180 - Z) - 90 = Y + Z - 90
4) X = 180 - Y - Z = Y + Z - 90 => 2Y + 2 Z = 270 => X+Z = 270/2 = 135
5) X = 180 - (Y+Z) = 180 - 135 = 45

Hope it helps. Good luck! :D

[wishmeluck]

Thanks so much!