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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
avatar+1718 
0

Here is the image:

 Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
 #2
avatar+128 
0

its not 120

Saketh  Aug 31, 2019
 #3
avatar+1718 
0

Ok, I know, I just checked, I'm SO SORRYYYYYYYYYYYYYYYYYYYYYYY

tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
 #4
avatar+1718 
0

The answer is around 120 though...

tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
 #5
avatar+1718 
+1

The answer is 115 right?

tommarvoloriddle  Aug 31, 2019
edited by tommarvoloriddle  Aug 31, 2019
 #6
avatar+1718 
0

Hello?

tommarvoloriddle  Aug 31, 2019
 #7
avatar+105238 
+2

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

 

 

cool cool cool

 Aug 31, 2019
 #8
avatar+1718 
+1

yay I got it right bu the user is not responding.

tommarvoloriddle  Aug 31, 2019

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