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

Question

A diagonal of a rectangle is inclined to one side of the rectangle at 25 The acute angle between the diagonals is A 55 B 50 C 40 D 25

Accepted Answer

B 50 Explanation According to the question A diagonal of a rectangle is inclined to one side of the rectangle at 25 ie 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 ie AC BD Dividing RHS and LHS by 2 AC BD Since O is midpoint 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

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