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# 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

+1
452
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+1438

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?

#1
+8963
+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

Feb 2, 2018

#1
+8963
+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
#2
+1438
+4

Thank you so much!