Question

3
select the correct answer.
\\(\overleftrightarrow{ab}\\) and \\(\overleftrightarrow{cd}\\) are parallel. what is \\(m\angle 5\\)?
image of two parallel lines ab and cd cut by a transversal, with angles labeled 1,2,3,4,5,6,7,8 and a 80° angle at angle 2
a. 120°
b. 30°
c. 80°
d. 100°

Explanation:

Step1: Find m∠2's supplementary angle

∠2 and the adjacent angle (∠1 or ∠3/∠4 related) form a linear pair? Wait, ∠2 is 80°, so ∠4 (vertical or adjacent?) Wait, AB and CD are parallel, transversal is the line. ∠2 and ∠4: no, ∠2 and ∠3 are adjacent? Wait, ∠2 and ∠4: actually, ∠2 and ∠4 are vertical? No, ∠2 and ∠3 are adjacent, forming a linear pair? Wait, ∠2 is 80°, so ∠3 (adjacent) would be 180 - 80 = 100°? Wait, no, ∠2 and ∠4: maybe ∠2 and ∠6 are corresponding? Wait, AB || CD, transversal. So ∠3 and ∠5 are same - side interior? No, ∠3 and ∠5: wait, ∠2 and ∠4: let's correct. ∠2 is 80°, so ∠4 (vertical angle? No, ∠2 and ∠4: actually, ∠2 and ∠4 are vertical? Wait, the transversal intersects AB at a point, creating angles 1,2,3,4. ∠2 and ∠4 are vertical? No, ∠1 and ∠3 are vertical, ∠2 and ∠4 are vertical. Wait, no, when two lines intersect, vertical angles are equal. So ∠1 = ∠3, ∠2 = ∠4. Then, AB || CD, so ∠3 and ∠5 are same - side interior? No, ∠3 and ∠5: wait, ∠3 and ∠5 are same - side interior? No, ∠3 and ∠5: actually, ∠3 and ∠5 are consecutive interior angles? Wait, no, ∠3 and ∠5: if AB || CD, then ∠3 and ∠5 are same - side interior angles, which are supplementary? Wait, no, ∠3 and ∠5: let's see, ∠2 is 80°, so ∠3 (adjacent to ∠2) is 180 - 80 = 100° (since they form a linear pair). Then, AB || CD, so ∠3 and ∠5 are same - side interior angles? No, ∠3 and ∠5: wait, ∠3 and ∠5 are actually alternate interior angles? No, ∠3 and ∠5: if AB || CD, then ∠3 and ∠5 are same - side interior, so they should be supplementary? Wait, no, ∠3 and ∠5: let's look at the diagram. Angles 3,4 are below AB, angles 5,6 below CD. So ∠3 and ∠5 are same - side interior? Wait, no, ∠3 and ∠5: when AB || CD, transversal, ∠3 and ∠5 are same - side interior, so m∠3 + m∠5 = 180°? Wait, no, that can't be. Wait, maybe ∠2 and ∠6 are corresponding angles. So ∠2 = ∠6 = 80°, then ∠5 and ∠6 are supplementary (linear pair), so m∠5 = 180 - 80 = 100°. Alternatively, ∠2 and ∠4 are vertical (wait, no, ∠2 and ∠4: if the transversal intersects AB, then ∠1 and ∠3 are vertical, ∠2 and ∠4 are vertical. So ∠4 = ∠2 = 80°. Then, AB || CD, so ∠4 and ∠5 are same - side interior angles? No, ∠4 and ∠5: adjacent? Wait, ∠4 and ∠5: when AB || CD, ∠4 and ∠5 are same - side interior? No, ∠4 and ∠5: actually, ∠4 and ∠5 are consecutive interior angles, so they are supplementary. So m∠4 + m∠5 = 180°. Since m∠4 = 80° (because ∠4 = ∠2, vertical angles), then m∠5 = 180 - 80 = 100°.

Step2: Identify the correct option

Among the options, 100° is option D.

Answer:

D. 100°