Question

In tne diagram, the horizontal bars are parallel and the vertical bars are parallel. Find x and y

Answer 1

Let's begin by listing out the given information:

In the figure attached, we see a rectangular shape. In a rectangle, alternating angles are equal

From the diagram, we can develop the following 2 equations:

`\begin{gathered} 5x+4y=156 \\ 14x+4y=66 \end{gathered}`

We have to solve these equations simultaneously

`\begin{gathered} 5x+4y=156 \\ 14x+4y=66 \\ \text{Subtract the first }from\text{ the second, we have:} \\ 14x-5x+4y-4y=66-156 \\ 9x=-90 \\ x=-10 \\ \text{Substitute x = -10 into the first equation, we have:} \\ 5x+4y=156\Rightarrow5(-10)+4y=156 \\ -50+4y+156 \\ 4y=156+50 \\ 4y=206 \\ y=51.5 \end{gathered}`