Provide reasons for the proof.

Given:<2 ≅ <4

and <2 and <3 is supplementary

Prove: <1 ≅ <3

Statement Reason
1. < 2 ≅ <4 1. Given

2. m<2 = m<4 2. Angle congruence postulate

3. <2 and <3 are supplementary 3. Given

4. m<2 + m<3 = 180° 4. Definition of supplementary angles

5. <1 and <4 are supplementary 5.

6. m<1 + m<4 = 180° 6. Definition of supplementary angles

7. m<1 + m<4 = m<2 + m<3 7.

8. m<1 + m<4 = m<4 + m<3 8.

9. m<1 = m<3 9.

10. <1 ≅ <3 10.