+56 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.
+137 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
+56 I still don't understand how you got 32 for angle ACB. Could you explain it in more detail?
