SOLUTION: Assume PQRS is a regular parallelogram. If angle Q= 5x, angle R= 3x-2y and angle S= 3x+5y. Solve for the variables.

Algebra ->  Parallelograms -> SOLUTION: Assume PQRS is a regular parallelogram. If angle Q= 5x, angle R= 3x-2y and angle S= 3x+5y. Solve for the variables.      Log On


   

Question 1010933: Assume PQRS is a regular parallelogram. If angle Q= 5x, angle R= 3x-2y and angle S= 3x+5y. Solve for the variables.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Opposite angles (such as Q and S) are congruent (same measure),
so 5x=3x%2B5y<-->5x-3x=5y<-->2x=5y .
Adjacent angles (such as Q and R) are supplementary,
so if the measures given are in degrees,
5x%2B%283x-2y%29=180<-->8x-2y=180<-->4x-y=90<-->4x-90=y .
With those two equations,
system%282x=5y%2Cy=4x-90%29-->system%282x=5%284x-90%29%2Cy=4x-90%29-->system%282x=20x-450%2Cy=4x-90%29-->system%28-18x=-450%2Cy=4x-90%29-->system%28x=%28-450%29%2F%28-18%29%2Cy=4x-90%29-->system%28x=25%2Cy=4x-90%29-->system%28x=25%2Cy=4%2A25-90%29-->system%28x=25%2Cy=100-90%29-->highlight%28system%28x=25%2Cy=10%29%29