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

Saketh Aug 31, 2019

#1

#7**+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

CPhill Aug 31, 2019