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Solution to Parallel Lines & Angles Problem

In the applet below, the black lines are parallel. Interact with this applet for a few minutes, then answer the questions that follow. As you do, be sure to move the BIG GREEN POINT anywhere you'd like!
Questions: 1) How does the measure of the indicated angle relate to the measures of the pink angle and the blue angle? 2) What previously learned theorem justifies this fact? Explain in detail.