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Maths-

General

Easy

Question

The diagonals of a Rectangle ABCD meet at O. If $angle B O C equals 44 to the power of ring operator end exponent blank t h e n blank angle O A D equals$

136º
68º
34º
none of these

The correct answer is: 68º

To find $angle O A D$
We have
$∠ B O C + ∠ B O A = 18 0^{o}$ [Linear pairs]

$\Rightarrow 44 + ∠ B O A = 180$

$\Rightarrow ∠ B O A = 136$
Since diagonals of a rectangle are equal and they bisect each other.

Therefore, in $Δ O A B$ , We have
$O A = O B$
$\Rightarrow ∠ 1 = ∠ 2 [∴$ Angle opp. to equal sides are equal]

In $Δ O A B$ , we have
$∠ 1 + ∠ 2 + ∠ B O A = 180$
$\Rightarrow 2 ∠ 1 + 136 = 180$
$\Rightarrow 2 ∠ 1 = 44$

$\Rightarrow ∠ 1 = 22$

Since each angle of a rectangle is a right angle.
$∠ B A D = 90$

$\Rightarrow ∠ 1 + ∠ 3 = 90$
$\Rightarrow 22 + ∠ 3 = 90$

$\Rightarrow ∠ 3 = 68$

Hence, $∠ O A D = 68$

Hence option 2 is correct

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