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Byju's Answer
Standard IX
Mathematics
Triangle and Sum of Its Internal Angles
In the given ...
Question
In the given figure, AD bisects
∠BAC in the ratio 1 : 3 and AD = DB. Determine the value of x.
Figure
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Solution
In the figure,
∠
B
A
C
+
108
°
=
180
°
[
Linear
pair
]
⇒
∠
B
A
C
=
72
°
Now, divide
72
°
in the ratio 1 : 3.
∴
a
+
3
a
=
72
°
⇒
a
=
18
°
∴
a
=
18
°
and
3
a
=
54
°
Hence, the angles are 18
o
and 54
o
.
∴
∠
B
A
D
=
18
°
and
∠
D
A
C
=
54
°
Given,
A
D
=
D
B
⇒
∠
D
A
B
=
∠
D
B
A
=
18
°
In
∆
A
B
C
, we have:
∠
B
A
C
+
∠
A
B
C
+
∠
A
C
B
=
180
°
angle sum property
⇒
72
°
+
18
°
+
x
°
=
180
°
⇒
x
°
=
90
°
Therefore
,
x
=
90
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Q.
In the given figure, AD divides ∠BAC in the ratio 1 : 3 and AD = DB. Determine the value of x.