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PQR is an isosceles triangle such that PQ = PR. S is a poi

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EgmatQuantExpert
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PQR is an isosceles triangle such that PQ = PR. S is a poi [#permalink] PQR is an isosceles triangle such that PQ = PR. S is a poi   Updated on: 07 Aug 2018, 04:44
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Q. PQR is an isosceles triangle such that PQ = PR. S is a point on QR such that ∠ QPS \(=50^o\). T is a point on PR such that PS = PT. Find ∠ TSR.


    A. \(20^o\)
    B. \(25^o\)
    C. \(30^o\)
    D. \(35^o\)
    E. \(50^o\)


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B

Originally posted by EgmatQuantExpert on 27 Apr 2017, 00:03.
Last edited by EgmatQuantExpert on 07 Aug 2018, 04:44, edited 1 time in total.
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Re: PQR is an isosceles triangle such that PQ = PR. S is a poi [#permalink] PQR is an isosceles triangle such that PQ = PR. S is a poi   27 Apr 2017, 00:04
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Reserving this space to post the official solution. :)
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Re: PQR is an isosceles triangle such that PQ = PR. S is a poi [#permalink] PQR is an isosceles triangle such that PQ = PR. S is a poi   27 Apr 2017, 00:58
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As PS=PT, Triangle PST is an isoceles triangle and hence Angle PST=PTS=Z
So,angle SPT = 180-2Z


As PQ=PR, Triangle PQR is an isoceles triangle and hence Angle PQR=PRQ=Y

So In Triangle PQR => 2Y+50+180-2Z=180
=> 2Y+50-2Z=0
=> Y+25=Z

Now Since Sum of Interior opposite angles = Exterior adjacent Angle

Angle PQR + Angle QPS = Angle PST + Angle TSR
Y+50=Z+X
Y+50=Y+25+X
X=25

Answer is B
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Re: PQR is an isosceles triangle such that PQ = PR. S is a poi [#permalink] PQR is an isosceles triangle such that PQ = PR. S is a poi   27 Apr 2017, 01:10
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EgmatQuantExpert wrote:
Q. PQR is an isosceles triangle such that PQ = PR. S is a point on QR such that ∠ QPS \(=50^o\). T is a point on PR such that PS = PT. Find ∠ TSR.


    A. \(20^o\)
    B. \(25^o\)
    C. \(30^o\)
    D. \(35^o\)
    E. \(50^o\)


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)




please refer attached fig
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Re: PQR is an isosceles triangle such that PQ = PR. S is a poi [#permalink] PQR is an isosceles triangle such that PQ = PR. S is a poi   13 May 2022, 05:18
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Re: PQR is an isosceles triangle such that PQ = PR. S is a poi [#permalink]
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