Question

6. In the figure below, AB || CD.

Given the information in problem 4, what is the m ∠ 2?

Problem 4:
4.
In the figure above, AB || CD.
What is the measure of angle 3 in degrees if m ∠ 1 = 125?
The correct answer for 4 is 55.

Answer 1

∠2 = 55°

Explanation:

Given the linear pair of angles, ∠1 and ∠2, with ∠1 = 125°, you want the measure of angle 2.

Linear pair

Angles of a linear pair are supplementary, so ...

∠2 = 180° -∠1

∠2 = 180° -125°

∠2 = 55°

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Additional comments

Your problem 4 gives the measure of ∠3 as 55°. Angles 2 and 3 are vertical angles, so congruent to each other. This tells you immediately that ∠2 = 55° with no math involved. (If the lines are parallel, they are also congruent to corresponding angles 6 and 7.)

The measures of angles 1-4 are related to each other as congruent or supplementary, without regard to the lines being parallel. The parallelism of the lines only comes into play when you are relating angles 1–4 to angles 5–8.