Question

in parallelogram lmno, what are the values of x and y? o x = 11, y = 14 o x = 11, y = 25 o x = 55, y = 14 o x = 55, y = 25

Explanation:

Answer:

In a parallelogram, opposite - angles are equal. So, \(2x=3x - 55\).
Solve for \(x\):
\[

$$\begin{align*} 3x-2x&=55\\ x&=55 \end{align*}$$

\]
Also, adjacent - angles are supplementary. Let's assume the non - opposite angles \((2x)\) and \((5y)\) are adjacent. Then \(2x + 5y=180\).
Substitute \(x = 55\) into the equation: \(2\times55+5y=180\).
\[

$$\begin{align*} 110+5y&=180\\ 5y&=180 - 110\\ 5y&=70\\ y&=14 \end{align*}$$

\]
So the answer is \(x = 55,y = 14\) which corresponds to the third option: \(x = 55,y = 14\)