The problem in the image involves finding the value of $x$ in a rectangle based on the properties of its diagonals. Here’s the step-by-step breakdown:

1. Diagonals Bisect Each Other:

   • Since the diagonals of a rectangle bisect each other, we have the midpoint property: $WV = \frac{1}{2} WY$
   • Doubling both sides to find $WY$: $2(WV) = WY$
   • Substituting $WV = 2x + 1$ (from the given values): $2(2x + 1) = WY$ $4x + 2 = WY$

2. Diagonals are Congruent:

   • In a rectangle, the diagonals are congruent, so: $WY = XZ$
   • Substituting values for $WY$ and $XZ$ from the previous steps: $4x + 2 = 8 - 2x$
   • Solving for $x$:
     • Bring all $x$-terms to one side: $4x + 2x = 8 - 2$ $6x = 6$
     • Divide by 6: $x = 1$

Thus, the solution confirms that $x = 1$.

Would you like further details or have any questions?

Related Questions

1. How can we verify the congruency of diagonals in other quadrilaterals?
2. What are the properties of a rectangle that involve its diagonals?
3. Can this method be applied to parallelograms or other quadrilaterals?
4. What happens if $x$ does not satisfy the equation in such problems?
5. Why do diagonals in a rectangle bisect each other?

Tip: For any quadrilateral, understanding diagonal properties is crucial, as they often help identify the shape based on their behavior (e.g., bisecting each other, congruence).