Part 3/4:
- Observe Corresponding Angles: With the parallel line in place, we note that the angle formed at vertex A, which we label as ( \angle A ), has a corresponding angle on the parallel line. This corresponding angle will also measure ( \angle A ) because they are alternate interior angles.
Establishing the Sum
Continuing from the previous configurations:
- We now observe that along the straight parallel line, the angles formed at points B and C, namely ( \angle B ) and the corresponding angle, sum up to 180 degrees along with ( \angle A ).
By geometric definition, any straight line encompasses an angle total of 180 degrees:
[
\angle A + \angle B + \text{corresponding angle} = 180^\circ
]