powerprep #7

[dunkin77]

Hi,

By knowing that those two triangles are isoisoscales, how do we know the angle of X? Could anyone explain how to get the angle X?

Thank you!

[jayhawk2001]

1 tells us that angle(RSQ) = angle(SQR). Lets call this y.
Therefore angle(QRS) = 180 - 2y. In anycase, it is insufficient

2 tells us that angle (SUT) = angle (UST). Lets call this z.
Angle (STU) = 180 - 2z. Insufficient.

Combining 1 and 2,

x + y + z = 180 (3 angles together form the straight line).

Also, for triangle RPT, we have
90 + (180 - 2y) + (180 - 2z) = 180
y + z = 135

Subst y+z in the first equation, we can get x

Hence C