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Question 2
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

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Solution

AC=BD

12AC=12BD [dividing both sides by 2 ]

OA=OB [since, O is the mid - point of AC and BD]

2=1 [angles opposite to equal sides are equal]

=25 3=1+2 [exterior angles is equal to the sum of two opposite interior angles]

=25+25=50

Hence, the acute angle between the diagonals is 50.

Alternate Method

Given, in a rectangle ABCD,

ACD=25

CAB=25 Now, BCA=9025=65=DAC [alternate interior angles]

In rectangle, diagonals bisect each other.

OD = OB and OA = OC

So, ΔODC and ΔOAB are congruent. [by SSS congruence rule]

OBA=25=DCA [ by CPCT rule]

Now, AOD is exterior angle of ΔAOB.

AOD=OAB+OBA=25+25=50

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