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# help

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230
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+128

In the diagram below, PQ and TU are parallel, and Q, R, and S are collinear. If PQR=120 degress and TRS=55 degrees, then what is the degree measure of RTU?
https://latex.artofproblemsolving.com/8/7/d/87d85a75e2ae6eed4edb32265fdd475daa8b479a.png

Aug 31, 2019

#1
+1694
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Here is the image:

Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
#2
+128
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its not 120

Saketh  Aug 31, 2019
#3
+1694
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Ok, I know, I just checked, I'm SO SORRYYYYYYYYYYYYYYYYYYYYYYY

tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
#4
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The answer is around 120 though...

tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
#5
+1694
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tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
#6
+1694
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Hello?

tommarvoloriddle  Aug 31, 2019
#7
+109355
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Draw PV  perpendicular to TU  such that PV intersects TU  at W

Then....since PQ is parallel to TU.....then  angles QPW and TWP  = 90°

So...we have the irregular pentagon   QPWTR

And angle  TRQ  is supplemental to angle TRS....so its measure  = 180 - 55 = 125°

And the sum ot the interior angles of a pentagon  =  540....so

So

RQP  + QPW + PWT  + WTR +TRQ  =  540

120 + 90 + 90 + WTR + 125  = 540

425 + WTR  =  540

WTR  =  540 - 425

WTR =  115°  =  UTR

Aug 31, 2019
#8
+1694
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yay I got it right bu the user is not responding.

tommarvoloriddle  Aug 31, 2019