Hello there. To solve this question, we'll have to remember some properties about vertical angles.
Given two angles A and B, they are said to be vertical angles if and only if:
That is, their measures are the same.
In this question, we have that the angles A and B have measures respectively equal to:
[tex]m\angle A=\lparen2x-10)^{\circ\text{ }}=m\angle B=\left(x+8\right)^{\circ}[/tex]Solving this equation for x:
Subtract x on both sides of the equation. Add 10 in the same manner.
[tex]\begin{gathered} 2x-10-x+10=x+8-x+10 \\ x=18 \end{gathered}[/tex]Therefore we have the solution for x.
Now we plug this into A in order to find its measure:
[tex]m\angle A=\left(2\cdot18-10\right)^{\circ}=\left(36-10\right)^{\circ}=26^{\circ}[/tex]This is the answer to this question.
