There is something wrong with the third problem, if 2 of the three angels of the triangles formed are the same it means the third angles are the same meaning so why are the arcs different lengths?

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Nothing is wrong with this problem because no central angles are present.  If the vertex of the third angle in each triangle rested on the center of the circle, then you would be correct: congruent central angles must intersect congruent arcs.  However, nothing in the problem states that the intersection of those two chords is at the center of the circle.