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Byju's Answer
Standard IX
Mathematics
Each Angle of a Rectangle Is a Right Angle
The diagonals...
Question
The diagonals of a rectangle ABCD meet at O. If ∠𝐵𝑂𝐶 =
44
∘
, find ∠𝑂𝐴𝐷.
A
36
∘
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B
48
∘
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C
56
∘
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D
68
∘
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Solution
The correct option is
D
68
∘
ABCD is a rectangle and
∠
B
O
C
=
44
∘
[Given]
∠
A
O
D
=
∠
B
O
C
[Vertically opposite angles]
∠
A
O
D
=
∠
B
O
C
=
44
∘
∠
O
A
D
=
∠
O
D
A
[Since OD = OA, as length of diagonals in a rectangle are equal and diagonals bisect each other]
Since sum of the angles of a triangle is
180
∘
, then
So,
∠
O
A
D
=
1
2
×
(
180
∘
−
44
∘
)
=
68
∘
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0
Similar questions
Q.
The diagonals of a rectangle ABCD meet at O. If ∠𝐵𝑂𝐶 =
44
∘
, find ∠𝑂𝐴𝐷.
Q.
The diagonals of a rectangle ABCD meet at O. If ∠𝐵𝑂𝐶 =
44
∘
, find ∠𝑂𝐴𝐷.
Q.
The diagonals of a rectangle
A
B
C
D
meet at
O
. If
∠
B
O
C
=
44
∘
, find
∠
O
A
D
. [2 MARKS]
Q.
The diagonals of a rectangle ABCD intersect at O. If
∠
B
O
C
=
68
∘
, then
∠
O
D
A
is
Q.
The diagonals of a rectangle ABCD intersect at O. If
∠
B
O
C
=
68
∘
, then
∠
O
D
A
is
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