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Byju's Answer
Standard VII
Mathematics
Co-interior Angles Theorem
In the follow...
Question
In the following figure,
l
1
,
l
2
,
l
3
are parallel to each other. Find the value of
∠
B
D
C
if
∠
B
F
E
=
∠
B
C
D
=
50
∘
.
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Solution
Given
l
1
,
l
2
,
l
3
are parallel to each other and
∠
B
F
E
=
∠
B
C
D
=
50
°
.
From the figure,
∠
C
A
B
=
90
°
Then,
∠
C
A
B
=
∠
F
E
B
=
90
°
(Corresponding angles)
Taking the
△
B
E
F
by angle sum property,
∠
B
E
F
+
∠
B
F
E
+
∠
E
B
F
=
180
°
⇒
90
°
+
50
°
+
∠
E
B
F
=
180
°
⇒
140
°
+
∠
E
B
F
=
180
°
⇒
∠
E
B
F
=
180
°
−
140
°
=
40
°
In triangle ABC, by angle sum property, we have
∠
A
B
C
+
∠
B
C
A
+
∠
C
A
B
=
180
∘
40
∘
+
∠
B
C
A
+
90
∘
=
180
∘
∠
B
C
A
=
180
∘
−
130
∘
=
50
∘
Now,
∠
A
C
D
+
∠
B
D
C
=
180
°
( Co-interior angles)
∠
A
C
D
=
∠
B
C
A
+
∠
B
C
D
=
50
∘
+
50
∘
=
100
∘
⇒
100
°
+
∠
B
D
C
=
180
°
⇒
∠
B
D
C
=
180
°
−
100
°
=
80
°
Hence,
∠
B
D
C
=
80
°
.
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0
Similar questions
Q.
In the following figure,
l
1
,
l
2
,
l
3
are parallel to each other. Find the value of
∠
B
D
C
if
∠
B
F
E
=
∠
B
C
D
=
50
∘
.
Q.
In the following figure,
l
1
,
l
2
,
l
3
are parallel to each other. Find the value of
∠
B
D
C
if
∠
B
F
E
=
∠
B
C
D
=
50
∘
.
Q.
Consider the following statements relating to 3 lines
L
1
,
L
2
and
L
3
in the same plane
(1). If
L
2
and
L
3
are both parallel to
L
1
, then they are parallel to each other.
(2). If
L
2
and
L
3
are both perpendicular to
L
1
, then they are parallel to each other.
(3). If the acute angle between
L
1
and
L
2
is equal to to acute angle between
L
1
and
L
3
, then
L
2
is parallel to
L
3
.
Of these statements:
Q.
The representation of
l
1
parallel to
l
2
and
l
3
perpendicular to
l
2
is respectively,
Q.
AB, AC are tangents to a parabola
y
2
=
4
a
x
If
l
1
,
l
2
.
l
3
are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then
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