document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #626471 by KMST(5328) $\"\"$ $\"About$

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Opposite angles (such as Q and S) are congruent (same measure),
\n" ); document.write( "so $\"5x=3x%2B5y\"$ <--> $\"5x-3x=5y\"$ <--> $\"2x=5y\"$ .
\n" ); document.write( "Adjacent angles (such as Q and R) are supplementary,
\n" ); document.write( "so if the measures given are in degrees,
\n" ); document.write( " $\"5x%2B%283x-2y%29=180\"$ <--> $\"8x-2y=180\"$ <--> $\"4x-y=90\"$ <--> $\"4x-90=y\"$ .
\n" ); document.write( "With those two equations,
\n" ); document.write( " $\"system%282x=5y%2Cy=4x-90%29\"$ --> $\"system%282x=5%284x-90%29%2Cy=4x-90%29\"$ --> $\"system%282x=20x-450%2Cy=4x-90%29\"$ --> $\"system%28-18x=-450%2Cy=4x-90%29\"$ --> $\"system%28x=%28-450%29%2F%28-18%29%2Cy=4x-90%29\"$ --> $\"system%28x=25%2Cy=4x-90%29\"$ --> $\"system%28x=25%2Cy=4%2A25-90%29\"$ --> $\"system%28x=25%2Cy=100-90%29\"$ --> $\"highlight%28system%28x=25%2Cy=10%29%29\"$ \n" ); document.write( "

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