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.

somebodyIUsedToKnow Apr 28, 2023

#1**+1 **

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

acyclics Apr 28, 2023

#2**0 **

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

somebodyIUsedToKnow
Apr 28, 2023