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Byju's Answer
Standard VIII
Mathematics
Rhombus
ABCD is a rho...
Question
ABCD is a rhombus,
∠
A
D
C
=
53
∘
. Diagonals AC and BD intersect at O. Find
∠
D
A
O
. [3 MARKS]
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Solution
Concept: 1 Mark
Application: 2 Marks
In a rhombus, diagonals bisect the interior angles.
∠
A
D
O
=
1
2
(
∠
A
D
C
)
∠
A
D
O
=
1
2
×
53
∘
[Substitute]
∠
A
D
O
=
26.5
∘
∠
A
O
D
=
90
∘
[Diagonals intersect at right angles]
In
△
A
O
D
,
∠
A
O
D
+
∠
A
D
O
+
∠
D
A
O
=
180
∘
[Angle sum property]
⇒
90
∘
+
26.5
∘
+
∠
D
A
O
=
180
∘
⇒
∠
D
A
O
=
180
∘
−
90
∘
−
26.5
∘
=
63.5
∘
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The diagonals AC and BD of a rhombus ABCD intersect at point O. Find m∠AOD and m∠BOC.