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555-605 (Medium)|   Geometry|      
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In the below diagram which is not drawn to scale QR=RP=PS 02 Oct 2013, 17:58
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A
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Difficulty:

25% (medium)

Question Stats:

86% (03:19) correct 14% (02:45) wrong based on 85 sessions

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In the below diagram which is not drawn to scale QR = RP = PS. Angle TPS measures 108 degrees. What is the measure of angle PRS?

A. 72
B. 75
C. 80
D. 85
E. 90
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A

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In the below diagram which is not drawn to scale QR=RP=PS 02 Oct 2013, 20:02
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Answer is Option A, 72 degrees.

guerrero25
In the below diagram which is not drawn to scale QR=RP=PS
Angle TPS measures 108 degrees
What is the measure of angle PRS?


A)72
B)75
c)80
D)85
E)90
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In the below diagram which is not drawn to scale QR=RP=PS 02 Oct 2013, 21:02
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Nice solution. Bunuel type :)
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In the below diagram which is not drawn to scale QR=RP=PS 02 Oct 2013, 21:13
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Nice solution. Bunuel type :)
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Awww thank you for the compliment! But I highly doubt I'll be able to match Bunuel - Bunuel is impeccable! O:) But thanks mate, I do try my little best! :D
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In the below diagram which is not drawn to scale QR=RP=PS 14 Feb 2014, 04:49
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nice solution!

Here is how I did it:

TPS is 108 degrees, which means that SPQ is 180 - 108 = 72 degrees. Hence PRS has to be <= 72 degrees. Then I looked at the answer choices and saw that only A fulfilled this premise. Hence A.
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In the below diagram which is not drawn to scale QR=RP=PS 14 Feb 2014, 08:07
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Since QR = PR, then angle RQP = angle RPQ = x

Therefore angle QRP = 180 - 2x and angle PRS = 2x.

Now, since RP = SP, angle PRS = angle RSP = 2x. Therefore, angle RPS = 180 - 4x.

Finally RPQ + RPS + TPS = 180.

108 + (180 - 4x) + x = 180
-3x = -108
x = 36

Since angle PRS = 2x, angle PRS = 72. Answer choice A.
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In the below diagram which is not drawn to scale QR=RP=PS 18 Jul 2016, 10:51
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guerrero25
In the below diagram which is not drawn to scale QR = RP = PS. Angle TPS measures 108 degrees. What is the measure of angle PRS?

A. 72
B. 75
C. 80
D. 85
E. 90
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Attachment:
Untitled.jpg
Untitled.jpg [ 18.43 KiB | Viewed 5551 times ]
there are many approach to this one
consider fig.
b+e+108=180----------->b+e=72-------(A)
c=a+b(ext. angle of triangle)
c=2b(QR=RP)---------b=c/2-------(B)
also e= 180-(c+d)
e=180-2c (PR=PS)---------(C)
putting (B)& (C) in (A)
c/2+180-2c=72
c=PRS=72
Ans A
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In the below diagram which is not drawn to scale QR=RP=PS 06 May 2021, 11:01
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