Question

In the given figure, OR is the bisector of angle POS and OT is the bisector of angle OOS. If P, O and Q are colinear, then find the angle between OR and OT.​

Answer 1

Answer:

With

Step-by-step explanation:

Let ∠ AOC  =  2x 

So,

∠ AOD =  ∠ DOC  = x    

( As given OD is the bisector of ∠ AOC ) 

Let ∠ BOC  =  2y 

So,

∠ BOE  =  ∠ EOC  =  y                                               (  As given OE is bisector of ∠ BOC ) 

And,

∠ DOE  = 90°                                                              ( As given OD is perpendicular to OE  ) 

We can write ∠ DOE ,

As  : 

∠ DOE  =  ∠ DOC  + ∠ EOC  

∠ DOC  +  ∠ EOC  = 90​°               ------- ( 1 )                   ( As given ∠ DOE  = 90°   ) 

x  + y  =  90​°                                                               ( From our assumption )

∠ AOD  +  ∠ BOE  =  x  +  y  

So,

∠ AOD +  ∠ BOE  = ​ 90​°            --------- ( 2 )

Now we add equation 1 and 2 we get 

∠ DOC  +  ∠ EOC + ∠ AOD +  ∠ BOE = 180° 

So we can say that A , O and B are colinear .                         ( Hence proved)

I hope after that u will get ur ans

Answer 2

Answer:

90

Step-by-step explanation:

the bisectors are always equal

so we can take angle qot = angle sot

let them be x . ( first equation)

we can also take angle SOR = angle ROP

so let them be y. (second equation)

so by adding both the equations

x+x+y+y=180 (by linear pair)

so this will be 2(x+y)=180

x+y=180/2

x+y=90