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avatar+1146 

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

Best Answer 

 #1
avatar+7095 
+2

Looking at triangle  PQR....

 

RP  =  PQ    so    ∠QRP  =  ∠PQR  =  x°

 

x + x + 3y   =   180

 

2x + 3y   =   180

 

Looking at triangle SPQ....

 

∠SPQ  =  180 - 3y

 

x + 2y + (180 - 3y)  =  180

 

x - y + 180   =   180

 

x - y   =   0

 

x   =   y

 

Substitute  y  for  x  in the equation  2x + 3y  =  180

 

2y + 3y  =  180

 

5y  =  180

 

y  =  36

 

3y  =  3 * 36

 

3y  =  108

hectictar  Feb 2, 2018
 #1
avatar+7095 
+2
Best Answer

Looking at triangle  PQR....

 

RP  =  PQ    so    ∠QRP  =  ∠PQR  =  x°

 

x + x + 3y   =   180

 

2x + 3y   =   180

 

Looking at triangle SPQ....

 

∠SPQ  =  180 - 3y

 

x + 2y + (180 - 3y)  =  180

 

x - y + 180   =   180

 

x - y   =   0

 

x   =   y

 

Substitute  y  for  x  in the equation  2x + 3y  =  180

 

2y + 3y  =  180

 

5y  =  180

 

y  =  36

 

3y  =  3 * 36

 

3y  =  108

hectictar  Feb 2, 2018
 #2
avatar+1146 
+3

Thank you so much!


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