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Convex Quadrilateral And Intersection (Posted on 2007-10-03) Difficulty: 3 of 5
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.

See The Solution Submitted by K Sengupta    
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re: What am I doing wrong? | Comment 6 of 8 |
(In reply to What am I doing wrong? by nikki)

In your discussion, A and B are not points, but rather angles (you're taking trig functions of them). Angle A is merely angle STR, based on how you're using it in the law of sines as applied to triangle STR, and angle B is merely angle QTR, seeing as to how you are using it within triangle QTR.

That means that A and B are not points that are colinear, but rather that they are synonymous with point T. Rather than colinear so that they add up to 180, they, as angles, not points, are supplementary, being on the same side of diagonal SQ at point T.

So they do indeed add up to 180, and in fact angle A is indeed equal to angle PTQ, as being the vertical angle to it. However, though their sines are equal (as all supplementary angles share equal sines), A is 95 and B is 85. (sin(180-x) = sin(x)).

  Posted by Charlie on 2007-10-05 11:17:55

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