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In regular pentagon \(PQRST\),  X is the midpoint of segment ST. What is the measure of angle XQS in degrees?


 

ant101  Oct 8, 2018
 #1
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Draw QT  and QS

 

Angles TQP, SQT  and  SQR  will trisect the interior angle PQR

And PQR  = 108

 

So  ...angle  SQT  = 108 / 3   = 36

 

But...by symmetry....angle XQS  =  (1/2)angle SQT  = (1/2)36  = 18°

 

 

 

cool cool cool

CPhill  Oct 8, 2018

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