PQRS is a convex quadrilateral with diagonals PR and QS that intersect at the point T. It is known that, Angle QPR = 50o, Angle RPS = 60o, Angle RQS = 30o and Angle QSR = 25o
Determine Angle PTQ.
At first it looked easy, then it looked impossible, then I got it.
Call Angle PTQ by a. All other angles can be easily written in terms of a.
WLOG let PS=1 to set a scale
 by Law of Sines on Triangle PQS, RS=sin(155-a)/sin(60)
 by Law of Sines on Triangle PTS, TS=sin(60)/sin(a)
 Using TS from  and Law of Sines on TRS, RS=sin(60)/sin(155-a)
 and  show that RS is its own reciprocal, so RS=1
Therefore Triangle PRS is isosceles.
 60 = 155-a
 a = 95
Posted by Jer
on 2007-10-03 10:53:09