Two Congruent Angles and a Side Not Between Them

Are two congruent angles and the side between them enough for congruent triangles?
Given the initial values, how many triangles are possible?
Is there any side length you can use for a that will never allow a triangle?
Keeping the other values the same, is there any size for the red angle that will not allow a triangle?
Do you think two angles and a side not between them are enough to force triangles to be the same?
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– John McLain

Information: Two Congruent Angles and a Side Not Between Them