Question

Find the measures of the labeled angles. (x +116)° =..... ° (Type a whole number.) 5x = ....°(Type a whole number.)

Answer 1

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:

`\begin{gathered} x+116=5x \\ x-5x=-116 \\ -4x=-116 \\ x=(-116)/(-4) \\ x=29 \end{gathered}`

With the value of x, we can find the measure of both angles, as they have the same measure:

`5x=5\cdot29=145`

Answer:

(x +116)° = 145°

5x = 145°