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Byju's Answer
Standard IX
Mathematics
Cyclic Quadrilateral
The sum of pa...
Question
The sum of pairs of opposite angles of a cyclic quadrilateral is:
A
360
o
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B
90
o
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C
180
o
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D
60
o
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Solution
The correct option is
C
180
o
Sum of opposite angles of a cyclic quadrilateral is
180
o
Let
A
B
C
D
is cyclic quadrilateral.
To prove that
∠
A
+
∠
C
=
180
°
and
∠
B
+
∠
D
=
180
°
Construction: J
oin
O
B
and
O
D
.
We know that
∠
B
O
D
=
2
∠
B
A
D
...
(
The
angle
at the
centre is twice
the
angle
at the circumference )
⟹
∠
B
A
D
=
1
2
∠
B
O
D
.
Similarly, we can write
∠
B
C
D
=
1
2
∠
B
O
D
.
Now, add above two equations,
∠
B
A
D
+
∠
B
C
D
=
1
2
∠
B
O
D
+
1
2
∠
D
O
B
⟹
∠
B
A
D
+
∠
B
C
D
=
1
2
(
∠
B
O
D
+
∠
D
O
B
)
...(complete angle)
⟹
∠
B
A
D
+
∠
B
C
D
=
1
2
×
360
°
=
180
°
.
So we get,
∠
A
+
∠
C
=
180
°
And similarly
∠
B
+
∠
D
=
180
°
.
Hence,option
C
is correct.
Suggest Corrections
0
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