In other words, we are asked to create an angle equivalent to another angle when given a straight line and a point.

Prerequisite Knowledge Needed:[br][br]- Proposition 8 states that if two triangles have two equal sides and consist of equal bases, then their angles contained inside the triangle are also equal to their respective angle.[br][br]- Proposition 22 persists of creating a triangle given three straight lines[br][br]- Rectilineal means in relation to straight lines[br][br]1) Let AB be a given straight line, and let angle DCE be a given rectilineal angle labeled as alpha.[br][br]2) On straight lines CD and CE, let the points D and E be taken at random respectively to CD and CE.[br][br]3) Let points D and E be joined to form segment DE.[br][br]4) Using Proposition 22, we then create three straight lines equivalent to the three straight lines CD, CE, and DE. Using these three lines, we create triangle AFG in a way that CD is equal to AF, CE is equal to AG, and DE is equal to FG.[br][br]5) Since DC and CE are equal to the two sides FA and AG, and the base DE is equal to the base FG, we can use Proposition 8 and conclude that angle DCE, labeled as alpha, is equivalent to the angle FAG, labeled as beta.[br][br]6) Therefore, on the given straight line AB with point A on it, the rectilineal angle FAG has been constructed equal to the given rectilineal angle DCE.[br][br]...