Question

ABCD is a rectangle where AB> BC and the diagonals intersect at O.If angle BOC =74° then the ratio AB/BC will be:
a)4/3 b)5/4 c) 3/2 d) 5/3 ​

Answer 1

3/2 is the answer plase like this

Answer 2

Answer:

ANSWER

In △ABC,

⇒  ∠CAB+∠ABC+∠ACB=180  

o

.

⇒  30  

o

+90  

o

+∠ACB=180  

o

.

⇒  120  

o

+∠ACB=180  

o

.

∴  ∠ACB=60  

o

 

We know that, diagonals of rectangle are equal and bisect each other equally.

∴  AO=OC=BO=OD

In △ABO,

⇒  AO=BO

⇒  ∠OAB=∠ABO        [ Angle opposite to equal side are also equal ]

⇒  ∠OAB=∠ABO=30  

o

 

⇒  ∠OAB+∠ABO+∠BOA=180  

o

 

⇒  30  

o

+30  

o

+∠BOA=180  

o

.

⇒  ∠BOA=120  

o

.

⇒  ∠BOA=∠COD          [ Vertically opposite angle ]

∴  ∠COD=120  

o

 

⇒  ∠COD+∠BOC=180  

o

         [ Linear pair ]

⇒  120  

o

+∠BOC=180  

o

 

∴  ∠BOC=60  

o

.

⇒  ∠ACB=60  

o

,∠ABO=30  

o

,∠COD=120  

o

 and ∠BOC=60  

o

.

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