We know that the two angles with measures (x+116) and (5x) have the same measure, as they are vertical angles.
Then, we can write:
[tex]\begin{gathered} x+116=5x \\ x-5x=-116 \\ -4x=-116 \\ x=\frac{-116}{-4} \\ x=29 \end{gathered}[/tex]
With the value of x, we can find the measure of both angles, as they have the same measure:
[tex]5x=5\cdot29=145[/tex]
Answer:
(x +116)° = 145°
5x = 145°
