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brittbeck2
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Wed Apr 02, 2008 3:40 pm
- Location: New York
1. triangle QRS is isosceles, angles RQS and RSQ are equal. Let's call those angles y. Also angle PQS is 180-y. Not sufficient. Not enough info
2. triangle STU is isosceles, angles UST and SUT are equal. Let's call those angles z. Also angle SUP is 180-z. Not sufficient. Not enough info
1 and 2 together: we can put together 2 equations based on geometry principles:
x and the 2 angles adjacent add up to 180:
x+y+z = 180
the angles of the PQSU cuadrilateral add up to 360
90+x+PQS+SUP=360
or 90+x+(180-y)+(180-z)= 360
from x+y+z= 180, we get y=180-x-z, so
90+x+(180-(180-x-z))+(180-z)=360
90+x+(180-180+x+z) +(180-z)=360
90+x+180-180+x+z+180-z=360 (z's cancel out)
90+2x+180= 360
2x+270= 360
2x= 90
x=45
BOTH statements together are sufficient
note: there are 3 variables and 2 equations, this tempted me to choose E at first too, but you can solve due to cancelling out of terms...
hope i am right in my thinking
old geezer
