Given pallelogram abcd, find the lengths and angles required.

Well since it's a parallelogram, we know that the opposite sides are the same and the same side interior angles (the ones pictured) add up to 180.

So let's first solve the sides.

5x + 2 = 8x - 7

So the goal with these equations is to move all of the variables onto one side and all of the integers onto the other. We can do this by doing:

5x + 2 = 8x - 7
+7           +7
5x + 9 = 8x
-5x          -5x
9 = 3x
/3    /3

3=x
So now since we know what x is, we can do one of the equations to figure out what the sides are.

5 * 3 + 2 = 17
So both of those sides have a length of 17.

On to the angles.

2y + 50 + 3y + 40 = 180
We have a similar goal, to move all the integers onto one side and all the variables onto the other.

So, what we can do is

2y + 50 + 3y + 40 = 180
2y + 3y + 50 + 40 = 180
5y + 90 = 180
-90            -90
5y = 90
/5     /5
y = 18

And now we can plug that in to both of the equations to find out the measurements.

2 * 18 + 50 = 86 degrees
3 * 18 + 40 = 94 degrees

I hope I helped :)