Yes, it is possible for two triangles to have the same angle measures but not be congruent.
What is congruency?
If two triangles are congruent, this means they are the same shape and the same size.
One triangle can be bigger than another and still have the same angle measure. For example, if there are two equilateral triangles all the angles are 60 degrees.
But one triangle is having a side of 10 units and the other triangle is having a side of 20 units means the second triangle is bigger than the first but the angle for both the triangles is 60 degrees.
Therefore, it is possible for two triangles to have the same angle measures but not be congruent.
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