Measure it, or if it is marked by a letter or number and a different shape has the SAME letter or number then the angles are congruent. A congruent angle are angles that have the same measure. Thye sign that is used to show this is ~=(~on top of the =). For example, ABC ~=PQR. This means that angle ABC has the same measure as PQR.
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A triangle if not found congruent by CPCTC as CPCTC only applies to triangles proven to be congruent. If triangle ABC is congruent to triangle DEF because they have the same side lengths (SSS) then we know Angle ABC (angle B) is congruent to Angle DEF (Angle E)
The transitive property is if angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C.
HPE is an angle congruent to angle HRN.
TBP an angle congruent to angle PTB.
The Symmetric Property of Congruence: If angle A is congruent to angle B, then angle B is congruent to angle A. If X is congruent to Y then Y is congruent to X.