Question

question 5
janet is designing a frame for a client. she wants to prove to her client that m∠1 = m∠3 in her sketch. what is the missing justification in the proof?
statement justification
segment cd intersects segment ab given
∠1 + ∠2 = 180°
∠2 + ∠3 = 180°
∠1 + ∠2 = ∠2 + ∠3 transitive property
∠1 = ∠3 subtraction property
definition of supplementary angles
intersecting lines postulate
same - side interior angles theorem
vertical angles theorem

Explanation:

The angles ∠1 and ∠2, as well as ∠2 and ∠3, are linear - pairs (adjacent angles formed by two intersecting lines). By the definition of supplementary angles, two angles that form a linear - pair are supplementary (add up to 180°).

Answer:

Definition of Supplementary Angles