Need help on number 5

Question

asked Sep 10, 2021 50.3k views

1 Answer

Mert Inan · Answer 1 · 2021-09-17T01:21:48+0000

$m \angle 1 + m \angle 4 = 180^(\circ)$ is always true because angle 1 and angle 4 form a straight line. They are supplementary angles.
$m \angle 5 - m \angle 7 = 0$ is the same as
$m \angle 5 = m \angle 7$ which is always true since these two angles are vertical angles.
$z \perp y$ 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.
$\angle 2 \cong \angle 8$ 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
$m \angle 3$ with
$m \angle 1$ , and we can replace angle 4 with angle 2 as well, going from this
$m \angle 2 - m \angle 3 = m \angle 1 - m \angle 4$ to this
$m \angle 2 - m \angle 1 = m \angle 1 - m \angle 2$ . Next, rearrange things to get
$2(m \angle 2 - m \angle 1) = 0$ and that solves to
$m \angle 1 = m \angle 2$ . So the original claim is sometimes true. It all depends on if angles 1 and 2 are the same measure or not.