Remember that vertical angles are congruent and share a vertex. So, if given two angles that are vertical, you know that the measure of those angles is the same.
To solve for the value of two congruent angles when they are expressions with variables, simply set them equal to one another. This forms an equation that can be solved using algebra. After you have solved for the variable, plug that answer back into one of the expressions for the vertical angles to find the measure of the angle itself.
Sometimes in geometry problems you’ll be given more information than you actually need. The key to finding x in this problem is to remember that vertical angles must ne congruent. This ray here doesn’t really help you at all. You know that since these two angles share a common vertex right here and they’re on opposite sides of it, that they must be congruent. Since they’re congruent I can set these two equal to each other and it just becomes an algebra problem.
So 3x plus 2 will equal 8x minus 8, and I’m going to make my 8 a little clear I can do better than that and we just have this equation with variables on both sides. So I’m going to move 3x to the other side, since it’s positive I’m going to subtract 3 minus 3 is 0 so we have +2 equals 5x minus 8. Two step equation here I need to move that -8 to the other side. So -8 plus 8 is zero, 8 plus 2 is 10, 10 equals 5x and the last step is to divide by 5. So we get x must equal 2.
Two keys here, the first one is remember that your vertical angles must be equal and congruent. The second is to ignore the extraneous or extra information.