Final answer:
Two parallel lines intersected by a transversal with same side interior angles in a ratio of 1:14 yield angles of 12 degrees and 168 degrees. Four of each angle are formed, alternating along the lines and adding up to 180 degrees in each interior angle pair.
Step-by-step explanation:
When a transversal crosses two parallel lines, it forms eight angles. If the same side interior angles are in a ratio of 1:14, it means that the smaller angle and the larger angle add up to 180 degrees, because they are supplementary. Let's denote the smaller angle as x degrees and the larger angle as 14x degrees.
Since x + 14x = 180 degrees, we can calculate that 15x = 180 degrees. Dividing both sides by 15, we find that x = 12 degrees. Thus, the larger angle is 14 × 12 degrees, which equals 168 degrees.
Each pair of corresponding angles is equal, so we have two angles measuring 12 degrees and two measuring 168 degrees on each side of the transversal. This means that the other set of same side interior angles will also add up to 180 degrees and will also be 12 degrees and 168 degrees respectively. Therefore, all eight angles formed by the two parallel lines and the transversal measure 12 degrees, 168 degrees, 12 degrees, 168 degrees, 12 degrees, 168 degrees, 12 degrees, and 168 degrees, as they are alternating between the two parallel lines.