Question

Given that lines a and b are parallel, what angles formed on line a when cut by the transversal are congruent with ∠6?

Answer 1

I dont get what you mean by congruent but ∠2 and ∠3 and ∠7 and ∠6 are equal in measurments but if you mean by congruent that they ard facinv the same way the answer is d but if you mean by congruent that they are on the opposite side of the line the answer is c

Answer 2

Angle ∠6 will be the same magnitude =equal to angle ∠2 and angle ∠3

Further explanation

When parallel lines get crossed by a transversal some angles will be formed (which have the same magnitude = equal)) :

Corresponding Angles: The angles on the same corners

Alternate Interior Angles: Alternate sides of the Transversal, and on the Interior of the two crossed lines.

Alternate Exterior Angles: on the outer side of each of the two lines and on the opposite side of the transversal.

Then in the picture above:

Corresponding Angles: angles ∠1 & ∠5, ∠2 & ∠6, ∠3 & ∠7,∠4 & ∠8

Alternate Interior Angles: angles ∠4 & ∠5 and ∠3 & ∠6

Alternate Exterior Angles: angles ∠1 & ∠8, and ∠2 & ∠7

So that the angle ∠6 will be the same as the angle ∠2 (Corresponding Angles) and ∠3 (Alternate Interior Angles)

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Keywords: Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles, a transversal