In a triangle, the sum of all angles is always 180 degrees. If one angle measures 115 degrees, the remaining two congruent angles must add up to 180 - 115 = 65 degrees. Since these two angles are congruent, each one measures 65 / 2 = 32.5 degrees. Therefore, the measures of the angles in the triangle are 115 degrees and two angles of 32.5 degrees each.
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