Answer: [tex]\angle{2}=\angle{6}[/tex], because they are corresponding angles of parallel lines cut by a transversal.
[tex]\angle{5}=\angle{8}[/tex] 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, [tex]\angle{2}=\angle{6}[/tex]
Also, since [tex]\angle{5}\text{ and }\angle{8}[/tex] are vertical angles.
Vertical angles theorem says that vertically opposite angles at any cross section must be equal.
[tex]\angle{5}=\angle{8}[/tex] by Vertical angles theorem.
