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Standard IX
Mathematics
RS Agarwal
Question
In the figure, if
P
Q
∥
S
T
,
∠
P
Q
R
=
110
and
∠
R
S
T
=
130
, find
∠
Q
R
S
.
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Solution
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P
Q
∥
S
T
,
∠
P
Q
R
=
110
∘
and
∠
R
S
T
=
130
∘
Construction:
A line
X
Y
parallel to
P
Q
and
S
T
is drawn.
∠
P
Q
R
+
∠
Q
R
X
=
180
∘
(Angles on the same side of transversal.)
⇒
110
∘
+
∠
Q
R
X
=
180
∘
⇒
∠
Q
R
X
=
70
∘
Also
∠
R
S
T
+
∠
S
R
Y
=
180
∘
(Angles on the same side of transversal.)
130
∘
°
+
∠
S
R
Y
=
180
∘
∠
S
R
Y
=
50
∘
Now,
∠
Q
R
X
+
∠
S
R
Y
+
∠
Q
R
S
=
180
o
⇒
70
∘
+
50
∘
+
∠
Q
R
S
=
180
∘
∴
∠
Q
R
S
=
60
∘
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3
Similar Questions
Q1
In the figure, if
P
Q
∥
S
T
,
∠
P
Q
R
=
110
and
∠
R
S
T
=
130
, find
∠
Q
R
S
.
View Solution
Q2
In figure, if
P
Q
∥
S
T
,
∠
P
Q
R
=
110
o
and
∠
R
S
T
=
130
o
, find
∠
Q
R
S
.
View Solution
Q3
If
P
Q
∥
S
T
,
∠
P
Q
R
=
110
∘
and
∠
R
S
T
=
130
∘
find
∠
Q
R
S
.
View Solution
Q4
In the adjacent figure PQ || ST,
∠
P
Q
R
=
110
o
and
∠
R
S
T
=
130
o
, find
∠
Q
R
S
.
View Solution
Q5
If
P
Q
|
|
S
T
,
∠
P
Q
R
=
110
o
and
∠
R
S
T
=
130
o
, find
∠
Q
R
S
(
I
n
d
e
g
r
e
e
s
)
View Solution