Quadrilateral PQRS is shown. Quadrilateral P Q R S. Side P Q has length 6 b, side Q R has length 4 a plus b, side R S has length 11 b minus 10 a, and side S P has length 2 a plus 8. Angle P Q R has measure 6 x plus 13 degrees and opposite angle R S P has measure 7 x minus 5 degrees.

What must the values of a and b be for PQRS to be a parallelogram?


A= 2
B= 4

explanation:
This does look a little complicated at first, however, it is fairly simple once broken down. For this, you're going to have to go back to pre-algebra-like-thinking. You can use the fact that 6b+10a=11 b but set it up similar to this:

6b+10a=11b
-6b -6b
10a = 5b
and divide by a common factor of 5, and you get
2a=b
Now you can use this substitute for any place you see b in the equations represented, for example in the equations on the other pair of parallel sides (the parenthesis represent anywhere b is in the equation)

4a+(2a)= (2a)+8
6a= 2a+8
-2a -2a
4a=8

a=2

once you've got a=2 you can simply plug that into the ORIGINAL equality we made (2a=b)
2(2)=b
b=4