Question

In the figure, r//s

Answer 1

Answer:  $\angle{2}=\angle{6}$, because they are corresponding angles of parallel lines cut by a transversal.

$\angle{5}=\angle{8}$ by Vertical angles theorem.

Step-by-step explanation:

From the given picture, we can see there are two parallel lines r and s intersected by a transversal line t.

Since corresponding angles of parallel lines cut by a transversal.

Therefore they must be equal.

Then, $\angle{2}=\angle{6}$

Also, since $\angle{5}\text{ and }\angle{8}$ are vertical angles.

Vertical angles theorem says that vertically opposite angles  at any cross section must be equal.

$\angle{5}=\angle{8}$ by Vertical angles theorem.

Answer 2

M < 2 = m < 6...corresponding angles

m < 5 = m < 8....vertical angles are congruent