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NCERT Exemplar Solutions Class 9 Mathematics Solutions for Quadrilaterals - Exercise 8.1 in Chapter 8 - Quadrilaterals

Question 2 Quadrilaterals - Exercise 8.1

A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is

(A) 55º

(B) 50º

(C) 40º

(D) 25º

Answer:

(B) 50º

Explanation:

According to the question,

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

i.e., Angle between a side of the rectangle and its diagonal = 25°

Consider the acute angle between diagonals to be = x

We know that diagonals of a rectangle are equal in length i.e.,

AC = BD

Dividing RHS and LHS by 2,

⇒ ½ AC = ½ BD

Since, O is mid-point of AC and BD

⇒ OD = OC

Since, angles opposite to equal sides are equal

⇒ ∠y = 25°

We also know that,

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°.

Therefore, option (B) is the correct answer.

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