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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

by dunkin77 » Tue Apr 24, 2007 9:15 am

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!

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 24, 2007 9:15 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Tue Apr 24, 2007 9:45 pm

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

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