Question

the given figure PQ and Rs intersect at point P Q and q intersect at m&t and Rs intersect at point O if angle R is ratio angle r o m is equal to 1 ratio 5 and angle q and q ratio angle UNO is equal to 2 ratio 7 then the sum of X Y and Z are please tell urgenly needed​

Answer 1

Answer:

∠POR+∠POS=180  

o

 .....(1) (Linear pair of angles)

Ir is given that, ray OA and ray OB bisect ∠POR and ∠POS respectively.

Therefore,

∠POA=  

2

1

​  

∠POR and ∠POB=  

2

1

​  

∠POS

⇒∠POA+∠POB=  

2

1

​  

{POR+POS}

=  

2

1

​  

×180  

o

=90  

o

 (From equation 1)

Now, if ∠POA+∠POB=2:7

Sum of the ratios =2+7=9

then, we have ∠POA=  

9

2

​  

×90  

o

=20  

o

 

and ∠POB=  

9

7

​  

×90  

o

=70  

o

 

∠POR=2×∠POA=2×20  

o

=40  

o

 

∠SOQ=∠POR (Vertically opposite angles)

∴∠SOQ=40  

o

 

∠BOQ=∠BOS+∠SOQ

=∠POB+∠SOQ (Since, OB bisect ∠POS)

(∠BOS=∠POB)

=70  

o

+40  

o

=110  

o

 

∴∠BOQ=110  

o

Step-by-step explanation: