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Standard VI
Mathematics
Question
The given figure shows a square
A
B
C
D
and an equilateral triangle
A
B
P
. Calculate
∠
B
P
C
(in degrees)
65
o
85
o
70
o
75
o
A
65
o
B
70
o
C
85
o
D
75
o
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Solution
Verified by Toppr
Given that ABCD is a square &
△
APB is an equilateral triangle.
Hence
∠
P
A
B
=
∠
B
A
O
=
∠
A
B
P
=
∠
B
P
A
=
60
o
[ All interior angles of equilateral triangle are equal to
60
o
]
So
∠
P
B
C
=
∠
A
B
C
−
∠
A
B
P
=
90
o
−
60
o
=
30
o
Since PB=AB=BC so
△
PCB is a isosceles triangle.
So we get
∠
B
P
C
=
∠
B
C
P
[ Base angles of isosceles triangle are equal ]
Now in
△
PCB,
∠
B
P
C
+
∠
B
C
P
+
∠
P
B
C
=
180
o
⇒
2
∠
B
P
C
+
∠
P
B
C
=
180
o
⇒
2
∠
B
P
C
+
30
o
=
180
o
⇒
2
∠
B
P
C
=
180
o
−
30
o
⇒
2
∠
B
P
C
=
150
o
⇒
∠
B
P
C
=
150
o
2
⇒
∠
B
P
C
=
75
o
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Similar Questions
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The given figure shows a square
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C
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A
B
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View Solution
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In the given fig. ABCD is a square and
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