1) From the picture, we see that we have two vertical angles:
[tex]\begin{gathered} A=(3x+50)^{\circ} \\ B=(6x-10)^{\circ} \end{gathered}[/tex]
2) Now, because of the "Vertical Angles Postulate" from geometry, we know that angles A and B are equal, so equalling the angles and replacing by their expression from above, we get the following equation in terms of x:
[tex]\begin{gathered} A=B \\ 3x+50=6x-10 \end{gathered}[/tex]
3) We must solve the last equation for x, doing that we find:
[tex]\begin{gathered} 3x+50=6x-10 \\ 50=6x-10-3x \\ 50+10=6x-3x \\ 60=3x \\ x=\frac{60}{3} \\ x=20 \end{gathered}[/tex]
Steps to solve the equation
0) We have the equation:
[tex]3x+50=6x-10[/tex]
1) We want all the terms with x on one side, and the other on the other one. So we pass the term +3x to the right as -3x:
[tex]50=6x-10-3x[/tex]
2) Now we pass the term -10 to the left as +10:
[tex]50+10=6x-3x[/tex]
3) We sum the terms on each side:
[tex]60=3x[/tex]
4) We pass the 3 that multiplies the x on the right, dividing the 60 on the left:
[tex]x=\frac{60}{3}[/tex]
5) Finally we make the division and we get:
[tex]x=20[/tex]
Answer
x = 20
