In the diagram, two parallel lines are intersected by a transversal. What are the measurements of angles, 1, 2, 4, 5, 6, 7, and 8?

1, 6, 8 are each 55 degrees

2, 4, 5, 7 are each 125 degrees.

Step-by-step explanation:

We know 3 things that apply here:

1) When parallel lines are intersected by a transversal, the corresponding angles have the same measure. (the angles in the same position on the parallel line...2 and 4 are equal, 5 and 7 are equal, etc)

2)  Two angles that form a straight line equal 180 degrees

3) Angles that are opposite each other (vertical angles) in this situation are equal. (1 & 6 are equal, 4 & 7 are equal)

So what would be angle #3 is 55 degrees. That means the supplemental angle, #4 is 125 degrees.

Which makes angle 7 125 degrees and angle 8 55 degrees.

And then you apply these rules for angles 1, 2, 5 and 6.

Please let me know if you have any questions.

step-by-step explanation: