Math, asked by SAHILSONIKING, 1 year ago

The diagonals of a rectangle ABCD intersect at o. if, angle BOC = 70 degree find angle ODA

Answers

Answered by sukhad58
29
Given in rectangle ABCD, ∠BOC = 70°

∠BOC = ∠AOD  [Vertically opposite angles are equal]

∠AOD = 70°

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

We can write OA = OB = OC = OD

Hence DAOD is an isosceles triangle.

⇒∠OAD = ∠ODA  [Angles opposite to equal sides of a triangle are equal]

Let ∠OAD = ∠ODA = x

∠OAD + ∠ODA +∠AOD = 180°

 ⇒ x + x + 70° = 180°

⇒ 2x = 110°

 ⇒ x = 55°

Hence ∠ODA = 55°

 

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Answered by Arceus11
9
Refer to the figure above.
 <br />\angle BOC= \angle AOD\\<br />In \: \Delta AOD, \\<br />\angle AOD = \pi -2\angle OAD\\<br />2\angle OAD=180- 70\\<br />\angle OAD= \frac{110}{2}\\<br />\angle OAD=55
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