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Question
The diagonals of a rectangle ABCD meet at O, If ∠BOC = 44°, find ∠OAD.
Solution
The rectangle ABCD is given as:
We have,
∠BOC +∠BOA = 180° (Linear pair)
44° +∠BOA = 180°
∠BOA = 180° -44°
∠BOA = 136°
Since, diagonals of a rectangle are equal and they bisect each other. Therefore, in ΔOAB, we have
OA = OB (Angles opposite to equal sides are equal.)
Therefore,
∠1 = ∠2
Now,in ΔOAB, we have
∠BOA + ∠1 +∠2 = 180
∠BOA + 2∠1 = 180°
2∠1 = 44°
∠1 = 22°
Since, each angle of a rectangle is a right angle.
Therefore,
∠BAD = 90°
∠1+∠3 = 90°
22° +∠3 = 90°
∠3 = 68°
Thus, ∠OAD = 68°
Hence, the measure of∠OAD is 68°.
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