Answer:
Because linear pairs are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.
Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.
Explanation:
A linear pair is a pair of adjacent angles formed when two lines intersect. The two angles of a linear pair are always supplementary (that is they add up to 180°).
Therefore m∠1 and m∠2 are linear pairs, also m∠2 and m∠3 are linear pairs.
Hence:
m∠1 + m∠2 = 180°
m∠2 + m∠3 = 180°
Using substitution property:
m∠1 + m∠2 = m∠2 + m∠3
subtracting m∠2 from both sides:
m∠1 + m∠2 - m∠2 = m∠2 + m∠3 - m∠2
m∠1 = m∠3
∠1 and ∠2 are congruent
Because linear pairs are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.
Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.