Question

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

Explanation:

Step1: Use opposite - angles property

In a parallelogram, opposite angles are equal. So, \(\angle L=\angle N\) and \(\angle M=\angle O\). We have \(\angle O = 2x\) and \(\angle M=3x - 55\). Since adjacent angles in a parallelogram are supplementary (\(\angle O+\angle M = 180^{\circ}\)), we get the equation \(2x+(3x - 55)=180\).
\[2x+3x-55 = 180\]
\[5x-55 = 180\]
\[5x=180 + 55\]
\[5x=235\]
\[x = 47\] (This is wrong. Let's use the correct property: \(\angle O\) and \(\angle M\) are adjacent angles. The correct way is to use the property that opposite angles are equal. \(\angle O=\angle M\), so \(2x=3x - 55\))
\[3x-2x=55\]
\[x = 55\]

Step2: Use adjacent - angles property for \(y\)

Adjacent angles in a parallelogram are supplementary. Let's use \(\angle N\) and \(\angle M\). \(\angle N = 5y\) and \(\angle M=3x - 55\). Since \(x = 55\), \(\angle M=3\times55-55=165 - 55 = 110^{\circ}\). And \(\angle N\) and \(\angle M\) are adjacent, so \(5y+110 = 180\)
\[5y=180 - 110\]
\[5y=70\]
\[y = 14\]

Answer:

\(x = 55,y = 14\)