PQRS is a convex quadrilateral with diagonals PR and QS that intersect at the point T. It is known that, Angle QPR = 50^{o}, Angle RPS = 60^{o}, Angle RQS = 30^{o} and Angle QSR = 25^{o}
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
[1] by Law of Sines on Triangle PQS, RS=sin(155a)/sin(60)
[2] by Law of Sines on Triangle PTS, TS=sin(60)/sin(a)
[3] Using TS from [2] and Law of Sines on TRS, RS=sin(60)/sin(155a)
[1] and [3] show that RS is its own reciprocal, so RS=1
Therefore Triangle PRS is isosceles.
[4] 60 = 155a
[5] a = 95

Posted by Jer
on 20071003 10:53:09 