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In a parallelogram ABCD, AB = 54, BC = 78, AC2 — BD2 = 8,168. Find the following.
 - the angles ABCD
 - the diagonals AC and BD
 - the angles between the diagonals AC and BD
 

Thank you in advance.

 Apr 28, 2023
 #1
avatar+135 
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38 degrees

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∘

 

Making 39 degrees true

 Apr 28, 2023
 #2
avatar+56 
0

I still don't understand how you got 32 for angle ACB. Could you explain it in more detail?

somebodyIUsedToKnow  Apr 28, 2023

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