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None! If the angles are not congruent then the shapes are not similar of congruent. But that is not a problem. The angles of an equilateral triangle are not congruent to the angles of a square but that does not mean that you cannot work with equilateral triangles or squares!

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Q: What is the problem if angles are not congruent?
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What is the Congruent Supplements Theorem?

if two angles are supplements of congruent angles, then the two angles are congruent.


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Angles are congruent if they are equal. Corresponding angles in figures that are similar are congruent.


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