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Byju's Answer
Standard IX
Mathematics
The sides BA ...
Question
The sides BA and DC of the parallelogram ABCD are produced as shown in figure. Then
A
∠
a
=
∠
x
+
∠
y
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B
∠
a
=
∠
b
=
1
2
(
∠
x
+
∠
y
)
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C
∠
y
=
∠
a
−
∠
b
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D
∠
a
+
∠
b
=
∠
x
+
∠
y
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Solution
The correct option is
D
∠
a
+
∠
b
=
∠
x
+
∠
y
In the given figure, AB || DC
∴
∠
a
=
∠
x
⋯
(
1
)
[Alternate Interior Angles]
And
∠
b
=
∠
y
⋯
(
2
)
[Alternate Interior Angles]
Adding (1) and (2), we get
∠
a
+
∠
b
=
∠
x
+
∠
y
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Q.
Sides AB and CD of a quadrilateral ABCD are produced as shown in the following figure. Show that
∠
x
+
∠
y
=
∠
a
+
∠
b
.