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Triangle within a triangle and angles [#permalink]

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06 Oct 2009, 11:15

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D

E

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11% (03:15) correct
89% (01:47) wrong based on 15 sessions

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Hello, I am trying to understand the answer on this question. Any help would be great!! Added a file with the question and drawing. Hope you can see it. It is apparently there. thanks,

Attachment:

TriangleQPS.JPG [ 2.5 KiB | Viewed 2621 times ]

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR.

(1) The measure of angle QPR is 30°

(2) The sum of the measures of angles PQR and PRQ is 150°

Hello, I am trying to understand the answer on this question. Any help would be great!! Added a file with the question and drawing.

Attachment:

triangle.pdf

Hope you can see it. It is apparently there. thanks,

Q: <PRS-<PQR=?

(1) <QPR=30 --> in triangle QPR three angles sum=180=<QPR+<PQR+<PRQ -->180=30+<PQR+(180-<PRS) --> 30=<PRS-<PQR SUFFICIENT

(2) Basically the same information is given <PQR+<PRQ=150 --> <PQR+180-<PRS=150 --> 30=<PRS-<PQR SUFFICIENT

D.

OR:

(1) <QPR=30 --> an exterior angle of a triangle is equal to the sum of the opposite interior angles --> <PRS =<QPR + <PQR --> <PRS - <PQR = <QPR = 30. Sufficient.

Re: Triangle within a triangle and angles [#permalink]

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07 Oct 2009, 12:40

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This post received KUDOS

Another solution -

Let LPRS = x and LPQR = y. Question is asking to find what is the difference between LPRS and LPQR.

IN triable PQR, LQPR and LPQR are the interior angles, LPRS is the exterior angle opposite to LQPR and LPQR. There is a rule that Exterior angle of a triangle = sum of the opposite interiod angles.

==> LPRS = LPQR + LQPR. ==> x = y + LQPR ==> x - y = LQPR. So if we know the angle of LQPR, we can solve the question.

Clue 1 = Given LQPR = 30. This is eactly what we need to solve the question. So sufficient.

Clue 2 = LPQR + LPRQ = 150 ==> From this we can deduce that LQPR= 30(since sum of all the interior angles is 180. Again we know LQPR and hence is sufficient to solve the question.

Known angle QSP = 90 degree. We need to find difference between angle PQR and PRS. Let PQR be x degree and PRS be y degree. We need the value of (y-x) degree.

Statement A: angle QPR is 30 degree.

Using the exterior angle concept, we know that angle QPR + angle PQR = angle PRS.

=> 30 + angle PQR = angle PRS => 30 + x = y => y-x = 30 degree. Hence we have got the required angle. Sufficient.

Statement B: angle PQR and PRQ = 150 degree.

In the triangle QPR, sum of the interior angles is 180 degree. That is angle QPR + angle PQR + angle PRQ = 180 degree.

Hence angle QPR = 180 - 150 = 30 degree. Here we have got the same angle as the one mentioned in statement A. Also we have proved that Statement A is sufficient. Hence Statement B is also sufficient.

Answer is D.
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Thanks for the explanation...I am feeling very bad when I am unable to recollect the basic principles:( +1

Nothing to worry. With practice you should be able to recollect it comfortably. The trick is to not to look for the answer quickly but to keep prodding with the information presented in the question.
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