Question

HELPPP!!!

Given that lines a and b are parallel, what angles formed on line b when cut by the transversal are congruent with ∠2?
A) ∠5 and ∠6
B) ∠5 and ∠7
C) ∠6 and ∠7
D) ∠6 and ∠8

Answer 1

The answer is C) 6 and 7
6 is congruent to 2 because they are corresponding angles.
7 is congruent to 2 because it is a vertical angle to angle 6 and it is an alternate exterior angle with angle 2.

Hope this helps =)

Answer 2

Answer: C)
`\angle{6}\text{ and }\angle{7}`

Explanation:

We know that when a transversal line passes through two parallel lines, then the corresponding angles and alternate ( both interior and exterior ) angles are congruent.

From the given figure, lines a and b are parallel.

`\angle{2}=\angle{3}` [∵ Vertical angles are congruent]

Also,
`\angle{2}=\angle{6}` [∵ if a transversal passes through parallel lines then corresponding angles are congruent]

Also,
`\angle{2}=\angle{7}` [∵ if a transversal passes through parallel lines then alternate exterior angles are congruent]

Hence, the angles formed on line b when cut by the transversal are congruent with ∠2 are :-

`\angle{6}\text{ and }\angle{7}`