# Converse of Parallel Lines Theorem - Problem 2 3,499 views

By applying the converse of the corresponding angles parallel lines theorem, you can determine the angle measure of two angles so that the lines are parallel.

If the measures of the angles are given with expressions of variables, set these expressions equal to one another: recall that the parallel lines theorem says that corresponding angles of parallel lines are congruent. So, if these angles are congruent, the lines are parallel. Solve for y. Then, plug this value back into one of the expressions to get the measure of the angle needed for these lines to be parallel.

If we apply the Converse of the Corresponding Angles Parallel Lines Theorem, then we can determine what does y need to be for these lines to be parallel?

So if we set these two equal to each other which would mean that they’re congruent then we can assume that these two lines must be parallel. So let’s do that. Let’s say 110 minus y must equal your corresponding angle which is 120 minus 3y. So we’ve got some negative variables here, so to make it positive, I’m going to add 3y to both sides. So you’ve got 110 plus 2y is equal to 120, so if I subtract 110 from both sides, we find that 2y is equal to 10 which means y must be 5. So what value of y? Y must be 5.

If you’re interested 110 minus 5, that would mean that this angle would be 105 degrees and since these two are congruent, that means that this angle as well needs to be 105 degrees. Since they are corresponding and congruent, these two lines must be parallel.