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Byju's Answer
Standard IX
Mathematics
Alternate Angles Test
In the given ...
Question
In the given figure, if AB || CD || EF, PQ || RS,
∠
R
Q
D
=
25
∘
and
∠
C
Q
P
=
60
∘
, then
∠
A
R
S
is equal to
A
85
∘
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B
135
∘
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C
120
∘
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D
110
∘
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Solution
The correct option is
C
120
∘
We have PQ || RS. Produce PQ to M.
∠
C
Q
P
=
∠
M
Q
D
[Vertically opp.
∠
S
]
∴
60
∘
=
∠
1
+
25
∘
⇒
∠
1
=
35
∘
We have PQ || RS. Produce PQ to M.
∠
C
Q
P
=
∠
M
Q
D
[Vertically opp. angles]
∴
60
∘
=
∠
1
+
25
∘
⇒
∠
1
=
35
∘
∠
A
M
Q
=
∠
1
+
∠
R
Q
D
=
60
∘
[alternate angles]
∠
R
M
Q
+
∠
A
M
Q
=
180
∘
⇒
∠
R
M
Q
=
180
−
60
=
120
∘
Since PQ || RS,
∠
R
M
Q
=
∠
A
R
S
=
120
∘
[alternate angles]
Suggest Corrections
1
Similar questions
Q.
In the given figure, if AB || CD || EF, PQ || RS,
∠
R
Q
D
=
25
∘
and
∠
C
Q
P
=
60
∘
, then
∠
A
R
S
is equal to
Q.
In the given figure, if AB || CD || EF,
PQ || RS,
∠
R
Q
D
=
25
°
and
∠
C
Q
P
=
60
°
, then find
∠
Q
R
S
.
Q.
Question 1
In figure, if
A
B
|
|
C
D
|
|
E
F
,
P
Q
|
|
R
S
,
∠
R
Q
D
=
25
∘
a
n
d
∠
C
Q
P
=
60
∘
,
t
h
e
n
∠
Q
R
S
is equal to:
A)
85
∘
B)
135
∘
C)
145
∘
D)
110
∘
Q.
Question 1
In figure, if
A
B
|
|
C
D
|
|
E
F
,
P
Q
|
|
R
S
,
∠
R
Q
D
=
25
∘
a
n
d
∠
C
Q
P
=
60
∘
,
t
h
e
n
∠
Q
R
S
is equal to:
A)
85
∘
B)
135
∘
C)
145
∘
D)
110
∘
Q.
In the given figure, if AB || CD || EF, PQ || RS,
∠
R
Q
D
=
25
∘
and
∠
C
Q
P
=
60
∘
, then
∠
A
R
S
is equal to
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