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RRB NTPC Mains or Stage 2 Model Paper 7 with solutions
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© examsnet.com
Question : 12
Total: 120
Bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect each other at a point P. Which one of the following is correct ?
2
∠
A
P
B
=
∠
C
+
∠
D
∠
A
P
B
=
∠
C
+
∠
D
∠
A
P
B
=
180
°
–
(
∠
C
+
∠
B
)
∠
A
P
B
=
180
°
–
(
∠
C
+
∠
D
)
Validate
Solution:
(a) (a) quadrilateral ABCD, AP and BP are bisectors of ∠(A) and ∠(B), respectively.
∴
∠
A
P
B
=
180
°
–
[
1
2
∠
A
+
1
2
∠
B
]
We know that sum of all angles of a quadrilateral= 360°
⇒ ∠(A) + ∠(B) + ∠(C) + ∠D = 360°
∴
1
2
∠
A
+
1
2
∠
B
+
1
2
∠
C
+
1
2
∠
D
=
360
°
2
⇒
⇒
1
2
∠
C
+
1
2
∠
D
=
180
°
–
[
1
2
∠
A
+
1
2
B
]
⇒
1
2
(
∠
C
+
∠
D
)
=
∠
A
P
B
[from eq. (i)]
⇒
∠
(
c
)
+
∠
D
=
2
∠
A
P
B
© examsnet.com
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