Provide reasons for the statements Given: <1 and <3 are vertical angles.Prove: <1 ~= <3 Each of these will be used once in the reasoning section. Definition of supplementary angles, definition of a linear pair, substitution, subtraction property of equality, and definition of congruence.

Answer:3. Definition of linear pair.4. Definition of supplementary angles.5. Substitution.6. Subtraction property of equality.7. Definition of congruence.Step-by-step explanation:Reason 3:The angles are supplementary because the angles 1 and 2, 2 and 3 form a linear pair and thus because of the definition of linear pair, they are supplementary angles.Reason 4:The sum of angles of 1 and 2, 2 and 3 is equal to 180 because these pair of angles are supplementary angles. Supplementary angles are those angles whose sum is 180 degrees.Reason 5:[tex]m\angle 1+m\angle 2=180\\m\angle 2+m\angle 3=180[/tex]Substitute [tex]m\angle 2+m\angle 3[/tex] in place of 180 for the first sum.So, [tex]m\angle 1+m\angle 2=m\angle 2+m\angle 3[/tex]Reason 6:[tex]m\angle 1+m\angle 2=m\angle 2+m\angle 3[/tex].Since [tex]m\angle 2[/tex] is on either side of equality, we can subtract it using the subtraction property of equality and thus we get:[tex]m\angle 1=m\angle 3[/tex]Reason 7:As angle 1 is equal to angle 3, therefore by definition of congruence, these angles are congruent.So, [tex]m\angle 1\cong m\angle 3[/tex]