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Standard XII
Mathematics
Condition for Two Lines to Be Parallel
Question
In the given figure, line
R
T
is drawn parallel to
S
Q
. If
∠
Q
P
S
=
100
∘
,
∠
P
Q
S
=
40
∘
,
∠
P
S
R
=
85
∘
and
∠
Q
R
S
=
70
∘
, then
∠
Q
R
T
is
45
∘
85
∘
65
∘
90
∘
A
90
∘
B
65
∘
C
85
∘
D
45
∘
Open in App
Solution
Verified by Toppr
From
△
P
S
Q
, we have
∠
P
S
Q
=
180
∘
−
(
100
∘
+
40
)
=
40
∘
∴
∠
Q
S
R
=
85
∘
−
∠
P
S
Q
=
85
∘
−
40
∘
=
45
∘
Since
R
T
∣
∣
S
Q
, therefore
∠
T
R
X
=
45
∘
Now,
70
∘
+
x
∘
+
45
∘
=
180
∘
∴
x
∘
=
180
∘
−
115
∘
=
65
∘
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Similar Questions
Q1
In the given figure, line RT is drawn parallel to SQ. If
∠
Q
P
S
=
100
∘
,
∠
P
Q
S
=
40
∘
,
∠
P
S
R
=
85
∘
and
∠
Q
R
S
=
70
∘
, then
∠
Q
R
T
=
_
_
_
_
_
_
_
.
View Solution
Q2
In the given figure, line RT is drawn parallel to SQ. If
∠
Q
P
S
=
100
o
,
∠
P
Q
S
=
40
o
,
∠
P
S
R
=
85
o
and
∠
Q
R
S
=
70
o
, then
∠
Q
R
T
is:
View Solution
Q3
PQRS is a cyclic quadrilateral. Given
∠
QPS
=
73
o
,
∠
PQS
=
55
o
and
∠
PSR
=
82
o
, calculate
∠
QRS.
View Solution
Q4
In the given figure, if lines l and m are parallel, then x =
(a) 20°
(b) 45°
(c) 65°
(d) 85°