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Byju's Answer
Standard XII
Mathematics
Condition for Two Lines to Be Parallel
In the given ...
Question
In the given figure, find
∠
B
D
C
.
A
60
o
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B
75
o
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C
45
o
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D
50
o
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Solution
The correct option is
D
45
o
Let given quadrilateral
A
B
C
D
is a parallelogram.
Then,
A
B
is parallel to
C
D
and
A
D
is parallel to
B
C
(Opposite sides of parallelogram are parallel)
⇒
∠
DAB
=
∠
BCD (Opposite angles of parallelogram are equal)
Since, it is given that
∠
DAB
=
75
∘
.
Then,
∠
BCD
=
75
∘
---- (1)
⇒
∠
DBC = 60
∘
---- (2) (Given)
In
△
DCB,
∠
BDC +
∠
BCD +
∠
DBC
=
180
∘
∠
BDC + 75
∘
+ 60
∘
=
180
∘
[From (1) and (2) ]
∠
BDC
=
180
∘
- 135
∘
∴
∠
B
D
C
=
45
∘
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Condition for Two Lines to Be Parallel
Standard XII Mathematics
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