Need help on number 5

is always true because angle 1 and angle 4 form a straight line. They are supplementary angles. is the same as which is always true since these two angles are vertical angles. is sometimes true. There are many cases where it is not true, but it's not impossible for lines z and y to be perpendicular. is always true as these are alternate exterior angles. You can use a few options to prove this, but one way is to use angle 2 = angle 4 (vertical angles) and then angle 4 = angle 8 (corresponding angles). By the transitive property, angle 2 = angle 8. Angles 1 and 3 are congruent, so we can replace with , and we can replace angle 4 with angle 2 as well, going from this to this . Next, rearrange things to get and that solves to . So the original claim is sometimes true. It all depends on if angles 1 and 2 are the same measure or not.