Question

In the figure, r//s

<2= < _____?because they are corresponding angles of parallel lines cut by a transversal.
<5=<______? by the Vertical Angles Theorem.

Answer 1

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

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

Answer 2

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.

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.