Question

If ON = 8x - 8, LM = 7x + 4, NM = x - 5, and OL = 3y - 6, find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale. (Image is attached)thank you ! :)

Answer 1

Given the parallelogram:

ON and LM are equal, then:

$\begin{gathered} 8x-8=7x+4 \\ 8x-7x=4+8 \\ \Rightarrow x=12 \end{gathered}$

OL and NM are equal too:

$\begin{gathered} 3y-6=x-5 \\ 3y=12-5+6 \\ \Rightarrow y=\frac{13}{3} \end{gathered}$

Answer: x = 12 and y = 13/3