Question

If four parallel lines are intersected by one transversal, what is the sum of all angles on one side of the transversal only? I think it’s 720 degrees because there’s four supplementary angles and 180•4=720.

I just need clarification and can someone explain it to me how you could, I understand why, but don’t know how to explain it.

Answer 1

The sum of all the angles on one side of the transversal when four parallel lines are intersected by a transversal is 720 degrees. This happens because the angles form two full sets of supplementary angles, with each angle being counted twice except for the first and the last.

Step-by-step explanation:

When four parallel lines are intersected by a transversal, eight angles are formed on one side of the transversal. Each pair of corresponding angles between the parallel lines is congruent. Since each pair of adjacent angles formed by the transversal with the parallel lines is supplementary (adds up to 180 degrees), the sum of all angles on one side of the transversal is:

1. Angle 1 + Angle 2 = 180 degrees (supplementary)
2. Angle 2 + Angle 3 = 180 degrees (supplementary, Angle 2 is counted twice)
3. Angle 3 + Angle 4 = 180 degrees (supplementary, Angle 3 is counted twice)
4. Since Angle 1 and Angle 4 are also congruent to Angle 2 and Angle 3 respectively, they add up to 180 degrees again when considered with their adjacent angle.

So, we have two full sets of supplementary angles, which gives us:

180 degrees × 4 = 720 degrees

Therefore, the sum of all the angles on one side of the transversal is indeed 720 degrees, as you initially thought. However, it's important to note that each angle is counted twice except for the first and the last angle.