Answer:
3. Vertical angles are congruent.
4. Transitive Property of Equality.
Explanation:
The missing reasons in the proof are:
Vertical angles are congruent,Transitive Property of Equality.
Here is the completed proof:
Statements Reasons
22 and 23 are supplementary. | Given
21 and 22 form a linear pair. | Definition of linear pair
21 and 22 are supplementary. | Vertical angles are congruent.
21 + 22 = 180° | Definition of supplementary angles
21 + 23 = 180° | Property of Substitution
21 = 180° - 23° | Property of Subtraction
21 = 157° | Property of Substitution
Therefore, 21 and 24 are supplementary.
The Transitive Property of Equality states that if A = B and B = C, then A = C. In this proof, we use the Transitive Property of Equality to show that 21 = 157°.