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

Solution:

From the question,

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

Angle between a side of the rectangle and its diagonal = 25º

Consider x as the acute angle between diagonals

As the diagonals of a rectangle are of equal length

AC = BD

Divide LHS and RHS by 2

AC/2 = BD/2

Here O is the mid-point of AC and BD

OD = OC

Angles opposite to equal sides are equal

∠y = 25°

From the angle sum property of a triangle, exterior angle is equal to the sum of opposite interior angles

∠BOC = ∠ODC + ∠OCD

Substituting the values

∠x = ∠y + 25°

∠x = 25° + 25°

∠x = 50°

Therefore, the acute angle between the diagonals is 50°.

✦ Try This: A diagonal of a rectangle is inclined to one side of the rectangle at 55º. The acute angle between the diagonals is a. 55º, b. 50º, c. 40º, d. 25º

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8

---

NCERT Exemplar Class 9 Maths Exercise 8.1 Problem 2

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

Summary:

A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is 50°

---

☛ Related Questions:

• ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is a. 40º, b. 45º, c. 50º, d. 60º
• The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in or . . . .
• The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in or . . . .