Question

find the correct answers below. *
30 points
quadrilateral rtwv is shown with diagonals rw and tv that intersect at point m where rm = 4x, tm = (3y + 15), wm = 84, and vm = 75.
6 13 21 20 19 15 6.5 7.5 9
what value of x will make rtwv a parallelogram?
what value of y will make rtwv a parallelogram?
what is the length of vt?

Explanation:

Step1: Solve for x (parallelogram diagonal rule)

In a parallelogram, diagonals bisect each other, so $RM = WM$.
$4x = 84$
$x = \frac{84}{4} = 21$

Step2: Solve for y (parallelogram diagonal rule)

Diagonals bisect each other, so $TM = VM$.
$3y + 15 = 75$
$3y = 75 - 15 = 60$
$y = \frac{60}{3} = 20$

Step3: Find length of VT

VT is the sum of $VM$ and $TM$.
$VT = VM + TM = 75 + 75 = 150$
(Note: Since diagonals bisect, $TM=VM$, so we can also calculate as $2\times75$)

Answer:

What value of x will make RTWV a parallelogram? $\boldsymbol{21}$
What value of y will make RTWV a parallelogram? $\boldsymbol{20}$
What is the length of VT? $\boldsymbol{150}$