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Two Angles are Supplementary when they add up to 180°.

m∠2 + m∠1 = 180° (*)

If ∠1 ≅ ∠3, then m∠1 = m∠3.

Substitute to the (*)

m∠2 + m∠3 = 180°

Therefore ∠2 and ∠3 are supplementary.