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Byju's Answer
Standard IX
Mathematics
Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.
The bisectors...
Question
The bisectors of
∠
B
and
∠
C
of a triangle
A
B
C
meet at a point
O
.
If
∠
A
=
60
∘
,
then
∠
B
O
C
is :
A
30
∘
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B
60
∘
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C
90
∘
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D
120
∘
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Solution
The correct option is
D
120
∘
REF.Image
O
B
&
O
C
are angle bisector of
∠
B
&
∠
C
In
Δ
B
O
C
∠
1
+
∠
2
+
∠
B
O
C
=
180
∘
_________ (1)
(sum of all Angles of
Δ
)
e
q
(
1
)
×
2
2
∠
2
+
2
∠
2
+
2
∠
B
O
C
=
360
∘
∵
∠
A
B
C
=
2
∠
1
∠
A
B
C
+
∠
A
C
B
+
2
∠
B
O
C
=
360
∘
∠
A
C
B
=
2
∠
2
In
Δ
A
B
C
∠
A
B
C
+
∠
A
C
B
+
∠
B
A
C
=
180
∘
____________ (2)
eq. (2)-(3)
2
∠
B
O
C
−
∠
B
A
C
=
180
∘
given
∠
B
A
C
=
60
∘
2
∠
B
O
C
−
∠
B
A
C
=
180
+
60
2
∠
B
O
C
=
240
∠
B
O
C
=
120
∘
Suggest Corrections
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Similar questions
Q.
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
(a) 60°
(b) 120°
(c) 150°
(d) 30°