Parallelogram R S T U is shown. Diagonals are drawn from point R to point T and from point U to point S and intersect at point V. The length of line segment U V is (x minus 3) meters and the length of line segment V S is (3 x minus 13) meters. Quadrilateral RSTU is a parallelogram. What must be the value of x? 2 4 5 10

Answer:Option C.Step-by-step explanation:Given information: RSTU is a parallelogram, Digonals RT and SU intersect each other at point V, UV=(x-3) and VS=(3x-13).According to the properties of a parallelogram, the diagonals of a parallelogram bisect each other.Using the properties of parallelogram we can say that point V divides the diagonal SU in two equal parts, UV and VS.[tex]VS=UV[/tex][tex]3x-13=x-3[/tex]Subtract x from both sides.[tex]2x-13=-3[/tex]Add 13 on both sides.[tex]2x=10[/tex]Divide both sides by 2.[tex]x=5[/tex]Therefore, the correct option is C.