Final answer:
The given information indicates that angles 1 and 2 are supplementary. Using geometry principles, if these are alternate interior angles formed by a transversal of parallel lines, and they are supplementary, then the lines must be parallel. Hence, TS is parallel to BC.
Step-by-step explanation:
The question relates to angle relationships established when a transversal crosses parallel lines. The provided information signifies that m<1 + m<2 = 180, which indicates that angles 1 and 2 are supplementary. Supplementary angles are pair of angles whose measures add up to 180 degrees.
In geometry, one of the properties of a transversal of parallel lines is that alternate interior angles are equal. If lines TS and BC are parallel and line is the transversal, then angles 1 and 2 would be alternate interior angles.
Since they are supplementary (as per the given condition), it can be argued that TS is parallel to BC due to the principle of alternate interior angles being equal in parallel lines. This proves the given statement that TS is parallel to BC when m<1 + m<2 equals to 180 degrees.
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