Answer:
56, see step-by-step.
Step-by-step explanation:
1. AB is parallel to CD. 1. Given
BC is parallel to DE.
m<BAC=64 and m<CBA =56
2. m<BAC + m<CBA + m<BCA =180 2. The angles in a triangle add up to 180
3. 64+ 56+ m<BCA=180 3. Substitution property of equality.
4. 120 + m<BCA=180 4. Addition property of equality.
5. m<BCA=60 5. Subtraction property of equality.
6. BC is a transversal that cuts through parallel lines AB and CD.
6. Def. of transversal.
7. m<CBA = m<BCD 7. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
8. m<BCA+m>BCD+m<DCE= 180. 8. Angle addition postulate
9. 60+56+m<DCE=180. 9.substitution.
10. 116 + m<DCE =180 10. Addition property of equality.
11. M<DCE =64 11. Subtraction property of equality.
12. DC is a transversal that cuts through parallel line BC and DE.
12. Def of transversal.
13. m<EDC= m<BCD 13. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
14. m<EDC= 60. 14. Substitution property of equality.
15. m<EDC+m<DCE+m<Dec=180. 15. Angle addition postulate
16. 56+64+m<dec = 180.16 Substitution property of equality.
17. 120+ m<dec = 180. Addition property of equality.
18. m<dec = 60 18. Subtraction property of equality.
