Q. 24.8( 17 Votes )

A diagonal of a r

Answer :

Given: Angle between a side of rectangle and its diagonal = 25°

Let the acute angle between diagonals be x



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


AC = BD


Dividing both sides by 2,


1/2AC = 1/2BD


OD = OC [ O is mid-point of AC and BD]


⇒ ∠y = 25° [ angles opposite to equal sides are equal]


Now we know that, exterior angle is equal to the sum of two opposite interior angles.


BOC = ODC + OCD


x = y + 25°


x = 25° + 25°


x = 50°


Hence, the acute angle between diagonals is 50°.

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