Question

Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f?

A) m∠4 = 110° and m∠3 = 70°
B) m∠1 = 110° and m∠2 = 110°
C) m∠1 = 110° and m∠3 = 70°
D) m∠2 = 110° and m∠3 = 110°

Answer 1

Your answer is C.
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Answer 2

C) m∠1 = 110° and m∠3 = 70°

Explanation:

When two lines are cut by a transversal, the angles that occupy the same relative position are called corresponding angles; in turn, when the lines are parallel, the corresponding angles are congruent, that is, they have the same measure.

When two lines cut by a transversal are parallel, the sum of the external angle of one line plus the internal angle of the other line must be 180°.

This is the case of angles 1 and 3, where the former is external to lines a and b, and measures 110°. While angle 3 is internal to lines a and b, and measures 70°, so that they add up to 180°. As a reference, the same case is presented with angles 2 and 4.

In the figure, the pair of corresponding and congruent angles are:

∠1 and ∠4 = 110°

∠2 and ∠3 = 70°

So, the correct answer is option C.

C) m∠1 = 110° and m∠3 = 70°

Hope this helps!