1. The problem involves three parallelograms with algebraic expressions for their sides and diagonals. 2. For parallelogram SRUT, the sides are given as $2x + 15$ and $x + 15$. The equation $2x + 15 = 2x + 15$ is true for all $x$, but the handwritten work shows solving $2x - x = 15 - 15$ which simplifies to $x = 0$. 3. For parallelogram UXWV, the top sides are $9x + 15$ and $6x + 15$. Since opposite sides of a parallelogram are equal, set $9x + 15 = 6x + 15$. 4. Simplify the equation: $$9x + 15 = 6x + 15$$ Subtract $6x$ from both sides: $$9x - 6x + 15 = 15$$ $$3x + 15 = 15$$ Subtract 15 from both sides: $$3x = 0$$ Divide both sides by 3: $$x = 0$$ 5. For parallelogram VUST, the diagonals intersect at point E. The expressions for the segments are $TE = 4 + 2x$ and $EV = 4x - 4$. 6. Since diagonals of a parallelogram bisect each other, $TE = EV$. 7. Set the expressions equal and solve for $x$: $$4 + 2x = 4x - 4$$ Subtract $2x$ from both sides: $$4 = 2x - 4$$ Add 4 to both sides: $$8 = 2x$$ Divide both sides by 2: $$x = 4$$ 8. Now find $TE$ by substituting $x = 4$ into $TE = 4 + 2x$: $$TE = 4 + 2(4) = 4 + 8 = 12$$ **Final answer:** $$x = 4$$ $$TE = 12$$