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In the diagram, $P$ is on $RS$ so that $QP$ bisects $\angle SQR$. Also, $PQ=PR$, $\angle RSQ=2y^\circ$, and $\angle RPQ=3y^\circ$. What is the measure, in degrees, of $\angle RPQ$?

Guest Oct 14, 2018
 #1
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By the exteriror angle theorem, 3y = 2y + x  ⇒ 3y - 2y  = x ⇒  y  = x

 

And in triangle PQR, since PQ  = RQ, then angle PQR  = angle PRQ  = x

 

So

 

3y  + x  +  x =  180

 

And since  y = x

 

3x + x + x  = 180

 

5x  = 180

 

x = 36

 

So 3x  = 3y  =  3(36)   = 108°

 

 

cool cool cool

CPhill  Oct 14, 2018

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