SOLUTION
A quadrilateral is an isosceles trapeziod if and only if the diagonals are congruent
Since the quadrilateral ABCD is an isosceles trapeziod, then
[tex]|AC|=|BD|[/tex]
Recall that
[tex]\begin{gathered} AC=7x-21 \\ BD=5x+13 \end{gathered}[/tex]
Then we equate the expression above
[tex]\begin{gathered} 7x-21=5x+13 \\ Collect\text{ like terms } \\ 7x-5x=13+21 \\ Simplify\text{the expression} \\ 2x=34 \\ \text{Divide bothsides by 2 } \\ x=\frac{34}{2} \end{gathered}[/tex]
Therefore the value of x is
[tex]x=17[/tex]
Therefore x =17
The right option is C
