In the given isosceles trapezoid $ABCD$, diagonals $AC$ and $BD$ are drawn. One key property of an isosceles trapezoid is that the diagonals are congruent, meaning they have equal lengths.

Thus, we set the lengths of $AC$ and $BD$ equal to each other:

$AC = BD$

From the diagram: $7x - 21 = 5x + 13$

To solve for $x$, follow these steps:

1. Subtract $5x$ from both sides: $7x - 5x - 21 = 13$ $2x - 21 = 13$

2. Add 21 to both sides: $2x = 34$

3. Divide by 2: $x = 17$

Thus, the value of $x$ is $17$, which corresponds to option C.

Would you like a deeper explanation on this? Here are five related questions to enhance your understanding:

1. What are the key properties of an isosceles trapezoid, and how do they relate to diagonals?
2. How would the solution change if the trapezoid were not isosceles?
3. What other geometric properties are useful when dealing with trapezoids?
4. How can the Pythagorean theorem be used in trapezoid problems involving diagonals?
5. How do different types of quadrilaterals compare in terms of their diagonal properties?

Tip: In isosceles trapezoids, the congruence of diagonals is a helpful property that can often simplify problems involving algebraic expressions.