Answer:
The diagonal is 421.
Step-by-step explanation:
This is a difficult question. To find the diagonal, you need to find the base and the height of the square. After that, you need to make it a triangle, by using this equation; 
(A being area, B being base, and H being height) then find the length of the hypotenuse of the triangle, which I will do for you.
The B and H = 416. Plug it into the equation now;
Now that you have done that, we know that the area of our new triangle is 86,528.
The diagonal is: 
I don't get how it would be a system of equations.
What you do is multiply x and y by 4 so the new be point is (-36,24)
When I do what the problem statement says, I get 47° for the left angle and 58° for the right one. They are not congruent.
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