in the given figure what are the respective measure of angle bae and angle cad
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bae =  45
ie..abd+fba=180 (linear pair)
abd=50
in triangle abe,
abe= 50 (given)
aeb=85 (given)
abe+aeb+bae= 180 (ASP of triangle)
50+85+bae=180
therefore bae =45

cad = 45
ie....ad=ae....therefore aed=ade=85 (angles opposite equal angles are equal)
in triangle ade,
ade+aed+dae=180 (ASP of triangle)
85+85+dae=180
therefore dae =10 (let us take as 1)
in triangle ace,
aec+aed=180 (linear pair)
therefore aec=95
ace = 50 (given)
...so ace+aec+eac=180 (ASP of triangle)
95+50+eac=180
therefore eac=35(let us take it as 2)

therefore angle cad = dae+cae
from 1 and 2,
dae +cae=cad
10+35=45
therefore cad=45