The diagonals of a rectangle ABCD intersect at o. if, angle BOC = 70 degree find angle ODA
Answers
Answered by
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°
∠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°
Attachments:
Answered by
9
Refer to the figure above.
Attachments:
Similar questions
History,
6 months ago
World Languages,
6 months ago
Social Sciences,
6 months ago
Math,
1 year ago
Social Sciences,
1 year ago
Hindi,
1 year ago