Question

$\large\underline{\bf{Question}}$

A diagonal of a rectangle is inclined to one side of the rectangle at 25°.The acute angle between the diagonal is:​

Answer 1

Answer

In △BOC,

∠OBC=∠OCB (Opposite angle of isosceles triangle)

∠OBC+∠OCB+∠BOC=180°

25° +25° +∠BOC=180°

Therefore, ∠BOC=130°

So, ∠AOB+∠BOC=180° (Linear pair)

∠AOB=180° −130°

∠AOB=50°

So, the acute angle between the diagonal is 50° .

HOPE IT HELPS YOU.

EVYAAN

Answer 2

$\huge\underline{\bf \red{Solution}}$

$\large\underline{\bf \red{ Given}}$

A diagonal of a rectangle is inclined to one side of the rectangle at 25º

So the angle between a side of the rectangle and its diagonal = 25°

Let us assume the acute angle between diagonals to be = x

We know that the diagonals of a rectangle are equal in length

AC = BD

On dividing RHS and LHS by 2,

⇒ 1/2 AC = 1/2 BD

Since O is the mid-point of AC and BD

⇒ OD = OC

Since angles opposite to equal sides are equal

⇒ ∠y = 25°

We also know that the angle sum property of the triangle exterior angle is equal to the sum of two opposite interior angles.

So, ∠BOC = ∠ODC + ∠OCD

⇒ ∠x = ∠y + 25°

⇒ ∠x = 25° + 25°

⇒ ∠x = 50°

Hence, the acute angle between diagonals is 50°.