The figure shows a trapezoid with sides 3x, 2x, 2x, 5x. Find x.

Let's solve the first problem.

: Find the value of $x$ in the figure below.

The figure shows a trapezoid with the following side lengths:

• Top parallel side: $3x$
• Bottom parallel side: $2x$
• Left non-parallel side: $2x$
• Right non-parallel side: $5x$

For a trapezoid to be constructible with these side lengths, and for $x$ to have a unique value without additional information (like perimeter or angles), it must be a special type of trapezoid. A common type of trapezoid in such problems is a tangential trapezoid, which means it has