Question

In the given the figure above, m∠BAC = 64° and m∠CBA = 56°. Part I: Find the m∠DEC. Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.

Answer 1

56, see 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.