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Lines PTQ and PUR are tangent to a circle, as shown below. If angle QTA = 41 degrees and angle RUA = 63 degrees, then find angle QPR, in degrees.

 

https://latex.artofproblemsolving.com/c/c/1/cc16b62c53fd72035896c4f0760d814431cc0883.png

 Mar 17, 2020
 #1
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arc(TA)  =  2·41o  =  82o

arc(AU)  =  2·63o  =  126o

arc(TAU)  =  82o + 126o  =  208o

arc(TU)  =  360o - 208o  =  152o

angle(QPR)  =  ½·(208o - 152o)  =  28o

 Mar 17, 2020

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