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Byju's Answer
Standard VIII
Mathematics
Angle in a Semicircle
In the given ...
Question
In the given figure,
O
is the centre of circle and
∠
B
O
D
=
150
o
. Find the value of
x
and
y
.
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Solution
It is given that
O
is the centre of a circle and
∠
B
O
D
=
150
o
We know that
Reflex
∠
B
O
D
=
(
360
o
−
∠
B
O
D
)
By substituting the values
Reflex
∠
B
O
D
=
(
360
o
−
150
o
)
By subtraction
Reflex
∠
B
O
D
=
210
o
Consider
x
=
1
/
2
( reflex
∠
B
O
D
)
By substituting the value
x
=
210
/
2
So we get
x
=
105
o
We know that
x
+
y
=
180
o
By substituting the values
105
o
+
y
=
180
o
On further calculation
y
=
180
o
−
105
o
By subtraction
y
=
75
o
Therefore, the value of
x
is
105
o
and
y
is
75
o
.
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Q.
In the given figure, O is the centre of the circle. If ∠BOD = 160°, find the values of x and y.