Step-by-step explanation:
Note:
The text below that are formatted in bold and underlined font are the solutions to the missing boxes in your given problem.
Explanation:
Given that ∠1, ∠2, ∠3, and ∠4 are formed by two intersecting segments, and that:
∠1 and ∠2 form a linear pair
∠2 and ∠3 form a linear pair
These linear pair relationships suggest that by the Linear Pair Postulate:
∠1 and ∠2 are supplementary. ⇒ Linear Pair Postulate
∠2 and ∠3 are supplementary. ⇒ Linear Pair Postulate
m∠2 + m∠ 3 = 180° ⇒ Definition of supplementary angles.
m∠1 + m∠3 = m∠2 + m∠ 3 ⇒ Substitution Property of Equality.
m∠1 = m∠3 ⇒ Subtraction Property of Equality.
