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If the angles are congruent, they will be less than 360 degrees.
The Vertical Angles Theorem says that a pair of vertical angles are always congruent.
if two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
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If three angles of one triangle are congruent to three angles of another triangle then by the AAA similarity theorem, the two triangles are similar. Actually, you need only two angles of one triangle being congruent to two angle of the second triangle.