Question

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is ? Please answer the question with explanation.​

Answer 1

Answer:

50°

Step-by-step explanation:

In a rectangle ABCD,

⇒ ∠ACD = 25°

⇒ ∠CAB = 25°

⇒ ∠BCA = 90° - 25° = 65° = ∠DAC

Now,

In rectangle, diagonals bisect each other.

OD = OB and OA = OC

So, ΔODC and ΔOAB are congruent.

∠OBA = 25° = ∠DCA

Now, ∠AOD is exterior angle of ΔAOB

⇒ ∠AOD = ∠OAB + ∠OBA

              = 25° + 25°

             = 50°

Therefore,

Acute angle between the diagonals = 50°

Hope it helps!