Question

Complete the following proof. You may use an answer more than once.
Given: <1 and <2 are complementary; <1 = <4
Prove: <3 and <4 are complementary

1: <1 and <2 are complementary/ Given
2: m<1 +m<2= 90/
3: <1=<4/Given
4: m<1 = m<4/ Definition of congruence
5: <2=<3/
6: m<2=m<3/ Definition of congruence
7: m<4 + m<3=90/

Choices are
Definition of Supplementary angles
Definition of linear pair
Substitution
Vertical Angle Therorem
Definition of complementary angles
Given

Answer 1

The proof can be completed using the steps as follows:

1: <1 and <2 are complementary/ Given
2: m<1 +m<2 = 90/ Definition of complementary angles
3: <1 = <4/ Given
4: m<1 = m<4/ Definition of congruence
5: <2 = <3/ Substitution (using step 3)
6: m<2 = m<3/ Definition of congruence
7: m<4 + m<3 = 90/ Definition of supplementary angles

Therefore, by definition of supplementary angles, <3 and <4 are complementary.