CAREFULLY draw a 2 in. segment on the dotted line below. Label the left endpoint A and the right endpoint B. Carefully measure and draw a 30 degree angle BAC from this segment AB. Now carefully (I'm catching a drift she wants us to be careful) measure and draw a 45 degree angle ABC from segment AB. Extend the sides of the angles if needed so a triangle is formed.

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Are you allowed to use a protractor to draw an angle? Or it's constructions with compass and straight edge only?

Sounds like she wants you to practice measuring angles using a protractor. Here's a rough sketch. The angles are not exact.

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