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Standard IX
Mathematics
Question
In the figure given below,
∠
Q
S
R
is equal to
65
o
50
o
70
o
75
o
A
50
o
B
65
o
C
70
o
D
75
o
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Solution
Verified by Toppr
Here,
m
∠
Q
P
R
=
50
∘
Also
∠
P
Q
O
=
∠
P
R
O
=
90
∘
....... known fact
∴
∠
P
Q
O
+
∠
P
R
O
+
∠
Q
P
R
+
∠
Q
O
R
=
360
∘
→
sum of all Angles
∴
90
∘
+
90
∘
+
50
∘
+
∠
Q
O
R
=
360
∘
m
∠
Q
O
R
=
360
−
90
−
90
−
50
∴
∠
Q
O
R
=
130
∘
Now,
∠
Q
S
R
=
1
2
(
∠
Q
O
R
)
→
angle substended at center is double by same arc at circumference
∴
∠
Q
S
R
=
1
2
×
130
∘
∴
m
∠
Q
S
R
=
65
∘
∴
∠
Q
S
R
=
65
∘
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Similar Questions
Q1
In the figure given below,
∠
Q
S
R
is equal to
View Solution
Q2
Refer to figure. Copy and complete the table :
∠
A
B
D
∠
D
B
E
∠
E
B
C
70
o
70
o
?
50
o
?
60
o
35
o
80
o
?
View Solution
Q3
In the given figure, ABCD is a parallelogram in which
∠
D
A
B
=
70
o
and
∠
D
B
C
=
65
o
, then find the measure of
∠
C
D
B
.
View Solution
Q4
In the given figure,
∠
B
A
D
=
65
o
,
∠
A
B
D
=
70
o
,
∠
B
D
C
=
45
o
(i) Prove that
A
C
is a diameter of the circle.
(ii) Find
∠
A
C
B
.
View Solution
Q5
In the given figure, ABC is a triangle with
B
C
∥
E
F
.
∠
A
E
F
=
50
o
and
∠
F
C
B
=
70
o
. Find
∠
A
,
∠
B
,
∠
F
.
View Solution