Question

in the given figure lines ab and CD intersect at the point of the sides CA and OBC have been produced to E and F respectively such that angle A is equal to X degree and Angle d b f is equal to Y degree if angle AOC a is equal to 80 degree angle C O A is equal to 40 degree and Angle B D O is equal to 70 degree then find the value of x degree + Y degree​

Answer 1

Answer:

From the figure we know that ∠AOD and ∠BOC are vertically opposite angles ∠AOD=∠BOC

It is given that

∠BOC+∠AOC=280

o

we know that ∠AOD=∠BOC

so it can be written as

∠AOD+∠AOD=180

o

2∠AOD=280

o

∠AOD=

2

180

∠AOD=∠BOC=140

o

From the figure we know that ∠AOC and ∠AOC form a linear pair

So it can be written as

∠AOC+∠AOD=180

o

substituting the values

∠AOC+140

o

=180

o

∠AOC=40

o

From the figure we know that ∠AOC and ∠BOD are vertically opposite angles

∠AOC=∠BOD=40

o

Therefore ∠AOC=40

o

, ∠BOC=140

o

, ∠AOD=140

o

, ∠BOD=40

o