in parallelogram lmno, mp = 21 m, lp=(y + 3) m, np=(3y - 1) m, and op=(2x - 1) m. what are the values of x…

in parallelogram lmno, mp = 21 m, lp=(y + 3) m, np=(3y - 1) m, and op=(2x - 1) m. what are the values of x and y? o x = 10 m, y = 1 m o x = 10 m, y = 2 m o x = 11 m, y = 1 m o x = 11 m, y = 2 m

in parallelogram lmno, mp = 21 m, lp=(y + 3) m, np=(3y - 1) m, and op=(2x - 1) m. what are the values of x and y? o x = 10 m, y = 1 m o x = 10 m, y = 2 m o x = 11 m, y = 1 m o x = 11 m, y = 2 m

Answer

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, $LP = NP$ and $MP=OP$.

Step2: Solve for y using $LP = NP$

Set up the equation $y + 3=3y - 1$. Subtract y from both sides: $3 = 2y-1$. Add 1 to both sides: $4 = 2y$. Divide both sides by 2: $y = 2$.

Step3: Solve for x using $MP = OP$

Set up the equation $21=2x - 1$. Add 1 to both sides: $22 = 2x$. Divide both sides by 2: $x = 11$.

Answer:

$x = 11\ m,y = 2\ m$