Answer:
x=9, y=5
Step-by-step explanation:
Solving for Y:
All diagonal vertices bisect (Split equally with) each other. So in this case, we have half of a vertex running from top right to bottom left that has 10 and 2y in it. The vertex is bisected by another vertex running from top left to bottom right. That means that 10=2y, and y=5. This property of bisecting vertices is true for all parallelograms, and since a square is a special parallelogram, it is true for it as well.
Solving for X:
Another property is that in a square, all the diagonals are equal in length and intersect each other at right angles. When you draw the diagonals in, they form 4 isosceles right triangles.
With a congruency proof, we can see that all angles bisected by a diagonal are 45 degrees. (Tell me if you need that proof as well)
Therefore we get 5x=45, x=9.
We also have a 2nd equation for x, and plugging x=9 in we also get 45 degrees, meaning our answer is right.
