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.
If I just focus on triangles SRQ, TSR, and TQR I get some of the following relationships:
sin30 sin25 sin25
------- = ------- so RQ = SR * -------
SR RQ sin30
sinA sin25 sin25
------- = ------- so TR = SR * -------
SR TR sinA
sin30 sinB sin30 sin25 sin30 sin25
------- = ------- so TR = RQ * ------- = SR * ------- * ------- = SR * -------
TR RQ sinB sin30 sinB sinB
So
sin25 sin25
TR = SR * ------- = SR * -------
sinA sinB
So sinA = sinB
So A = B
And since A and B are colinear, A+B = 180. So A=90.
But you guys all came up with 95 so I am sure you are right. Plus I didn't even use the other half of the rectangle. I basically solved for "you have triangle QRS with point T somewhere on QS. What are the angles at T?" which clearly cannot be solved only knowing the angles at S and Q. Yet somehow I came up with a number.
Do you guys see my mistake? Am I misinterpreting the description of the rectangle?
Edited on October 4, 2007, 4:45 pm
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Posted by nikki
on 2007-10-04 16:35:10 |
What am I doing wrong?
