Question

Geometry Question: Use the diagram to determine whether or not lines e and f are parallel.

Answer 1

From the given figure

Since the angles of measures (5x - 20) and (3x + 30) are vertically opposite angles

Since the vertically opposite angles are equal in measures, then

`5x-20=3x+30`

Now, we can find the value of x

Subtract 3x from both sides

`\begin{gathered} 5x-3x-20=3x-3x+30 \\ 2x-20=30 \end{gathered}`

Add 20 to both sides

`\begin{gathered} 2x-20+20=30+20 \\ 2x=50 \end{gathered}`

Divide both sides by 2

`\begin{gathered} (2x)/(2)=(50)/(2) \\ x=25 \end{gathered}`

Lines e and f could be parallel if the sum of the measures of the angles (2x + 10) and (3x + 30) equal to 180 degrees because they are in the interior position

Let us substitute x by 25 in each angle and find the sum of their measures

`\begin{gathered} 2x+10=2(25)+10=\mathring{60} \\ 3x+30=3(25)+30=\mathring{105} \\ 60+105=\mathring{165}\\e\mathring{180} \end{gathered}`

Since their sum is not equal to 180 degrees

Then lines e and f are not parallel