Answer:
Part 1) m<AEB=m<DEF
Part 2) [tex]m<AEB+m<BEC=90\°[/tex]
Part 3) [tex]m<AEC+m<CED=180\°[/tex]
Step-by-step explanation:
Part 1)
we know that
Vertical Angles are the congruent angles opposite each other when two lines cross
so
In this problem
m<AEB=m<DEF-----> by vertical angles
Part 2)
we know that
If the sum of two angles is equal to [tex]90\°[/tex] then the angles are complementary
In this problem
[tex]m<AEB+m<BEC=90\°[/tex] -----> by complementary angles
Part 3)
we know that
If the sum of two angles is equal to [tex]180\°[/tex] then the angles are supplementary
In this problem
[tex]m<AEC+m<CED=180\°[/tex] -----> by supplementary angles