The diagonals of a rectangle ABCD meet at O, If ∠BOC = 44°, find ∠OAD.
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°.
Concept: Angle Sum Property of a Quadrilateral
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The diagonals of a rectangle ABCD meet at O. If ∠ BOC =44∘, find ∠ OAD. [2 MARKS]
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In rectangle ABCD,
∠AOD=44∘ [vertically opposite]
∠ODA=∠OAD=x∘ [Since ΔOAD is an isosceles triangle)
∴ By the angle sum property of a triangle, we have
⇒∠OAD + ∠ODA + ∠AOD = 180∘
⇒x∘+x∘+44∘=180∘
⇒2x∘+44∘=180∘
⇒x∘=180∘−44∘2=136∘2=68∘
∴∠OAD=68∘
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