Converse of Parallel Lines Theorem - Problem 1
You can apply the Converse of the Parallel Lines Theorem to a problem like this which asks for what values of x are these lines parallel? Well first you have to ask what type of angles are these? Well they’re in between the lines and they’re on opposite sides of the transversal, so these are alternate interior angles.
If alternate interior angles are congruent or equal, then these 2 lines must be parallel. So to solve this all we have to do is set those 2 equal to each other. We can say that 4x is equal to x+10, so to solve this we’re going to subtract x, 3x is equal to 10 and if you divide by 3, you get x equals 10/3, so for what value of x are these lines parallel? 10/3 and what do we do? We said that if alternate interior angles are congruent, then these 2 lines must be parallel.