Maths-

General

Easy

Question

# The diagonals of a Rectangle ABCD meet at O. If

- 136º
- 68º
- 34º
- none of these

## The correct answer is: 68º

### To find

We have

$∠BOC+∠BOA=180_{o}$ [Linear pairs]

$⇒44+∠BOA=180$

$⇒∠BOA=136$

Since diagonals of a rectangle are equal and they bisect each other.
Therefore, in $ΔOAB$, We have

$OA=OB$

$⇒∠1=∠2[∴$ Angle opp. to equal sides are equal]

In $ΔOAB$, we have

$∠1+∠2+∠BOA=180$

$⇒2∠1+136=180$

$⇒2∠1=44$

$⇒∠1=22$

Since each angle of a rectangle is a right angle.

$∠BAD=90$

$⇒∠1+∠3=90$

$⇒22+∠3=90$

$⇒∠3=68$

Hence, $∠OAD=68$

$∠BOC+∠BOA=180_{o}$ [Linear pairs]

Since diagonals of a rectangle are equal and they bisect each other.

$OA=OB$

$⇒∠1=∠2[∴$ Angle opp. to equal sides are equal]

$∠1+∠2+∠BOA=180$

$⇒2∠1+136=180$

$⇒2∠1=44$

$∠BAD=90$

$⇒22+∠3=90$

Hence option 2 is correct

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