Question

When two lines intersect, the opposite angles are called vertical angles. Vertical angles have equal measures. Determine the measures of the vertical angles indicated in the figure to the right.

Answer 1

The measures of the vertical angles are 109 degrees and 109 degrees

Step-by-step explanation:

From the question, we're told that vertical angles have equal measures.

To be able to determine the measures of the vertical angles, we have to first determine the value of x by equating the measures of the vertical angles together and solving for x as seen below;

`\begin{gathered} 3x+70=8x+5\ldots\ldots\ldots\text{.(vertical angles have equal measures)} \\ \end{gathered}`

Let's subtract 70 from both sides of the equation;

`\begin{gathered} 3x+70-70=8x+5-70 \\ 3x=8x-65 \end{gathered}`

Let's subtract 8x from both sides of the equation;

`\begin{gathered} 3x-8x=8x-8x-65 \\ -5x=-65 \end{gathered}`

Let's divide both boh sides of the equation by -5;

`\begin{gathered} (-5x)/(-5)=(-65)/(-5) \\ x=13 \end{gathered}`

Since x = 13, we can now go ahead and determine the measures of the vertical angles as seen below;

`\begin{gathered} 3x+70=3(13)+70=39+70=109^(\circ) \\ 8x+5=8(13)+5=104+5=109^(\circ) \end{gathered}`

Therefore, the measures of the vertical angles are 109 degrees and 109 degrees.