Question

The diagonal of a parallelogram, ABCD intersects at 0,if angle BOC - 85°,angle - 30°and angle BDC - 65°,the angle DAC-
a) 10°
b) 20°
c) 40°
d) 65°​

Answer 1

Answer:Correct option is

C

38  

o

 

Step-by-step explanation:In given figure,

Quadrilateral ABCD is a parallelogram.

So, AD ∣∣ BC

∴ ∠DAC = ∠ACB  --- ( Alternate angle)

∴ ∠ACB = 32  

∘

 

∠AOB + ∠BOC = 180  

∘

  --- (straight angle)

⇒70  

∘

 + ∠BOC = 180  

∘

 

∴ ∠BOC = 110  

∘

 

In △BOC,

∠OBC + ∠BOC + ∠OCB = 180  

∘

 

⇒∠OBC  + 110  

∘

 + 32  

∘

 = 180  

∘

 

⇒ ∠OBC = 38  

∘

 

∴  ∠DBC = 38