Answer:
1. ∠1 and ∠3 are vertical angles (Given).
2. ∠1 and ∠2 form a linear pair.
∠2 and ∠3 form a linear pair. (Definition of linear pair)
3. ∠1 and ∠2 are supplementary.
∠2 and ∠3 are supplementary. (Theorem of linear pair angles, which states that if two angles are linear pair, the angles are supplementary.)
4. m∠1 + m∠2 = 180˚
m∠2 + m∠3 = 180˚ (Definition of supplementary angles)
5. m∠1 + m∠2 = m∠2 + m∠3. (Equalizing equations in statement 4).
6. m∠1 = m∠3 (Eliminating same angles at both sides of the equality).
7. ∠1 ≅ ∠3 (Definition of congruence).
The most important reason here is the theorem of linear pair angles, which was explain. Also, remember that supplementary angles are those which sum 180°. And congruence is defined as the equality between two magnitudes.
