Question

Given:
B
C
‾
∥
D
E
‾
BC
∥
DE
and
∠
A
B
C
∠ABC and
∠
A
E
D
∠AED are complementary.

Prove:
∠
A
B
C
∠ABC and
∠
A
C
B
∠ACB are complementary.

Answer 1

Answer:

See below for proof.

Step-by-step explanation:

BC ║ DE                                Given

m ∠ ABC = m ∠ADE                      If ║ lines, the corresponding angles are =

∠ABC and ∠AED are complementary     Given

m ∠ABC + m ∠AED = 90°             Definition of complementary angles

 m ∠ACB = m ∠AED                      If ║ lines, the corresponding angles are =

m ∠ABC + m ∠ACB  = 90°              Substitution  

∠ABC and ∠ACB are complementary    Definition of complementary angles