Question

Use your knowledge of angle pair relationships to write an equation and solve for x in the diagram.

Answer 1

According to the given graph, those are corresponding angles that are always congruent. So, we can elaborate on the following

`5x+7=9x-63`

Now, we solve for x, first, we subtract 7 on each side.

`\begin{gathered} 5x+7-7=9x-63-7 \\ 5x=9x-70 \end{gathered}`

Then, we subtract 9x on each side

`\begin{gathered} 5x-9x=9x-70-9x \\ -4x=-70 \end{gathered}`

We divide the equation by -4

`\begin{gathered} (-4x)/(-4)=(-70)/(-4) \\ x=(35)/(2) \end{gathered}`

Therefore, the solution is 35/2.