Question

if lines AB and CD intersects each other at O and angle AOC =42 , XO bisects angle BOC then angle XOD = ?​

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