Given that the indicated lines in the figure below are parallel, determine the sum of a+b+c without measuring the angles. Explain your reasoning in the style of a two-column proof.

Answer 1

We do not see any picture...
YOu have all three of your parallel line theorems such as
1) Alternate angles make a z pattern and under the arms of the z are equal
2) Corresponding angles make an F pattern, and under the arms of the F are equal
3) Interior Angles form a C pattern, and the angles inside the C add up to 180 degrees.
You also have vertically opposite angles that are equal.
Supplementary angles that share a straight line (and thus add up to 180 degrees).
Hope this is a big enough hint (as again we can't see the picture your textbook shows you)