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Byju's Answer
Standard VII
Mathematics
Parallel lines
In the figure...
Question
In the figure, ACE, BCF and DCG are straight lines and AB || HC.
Find the angles p,q,r and s.
A
p
=
45
∘
,
q
=
50
∘
,
r
=
65
∘
,
s
=
50
∘
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B
p
=
45
∘
,
q
=
65
∘
,
r
=
50
∘
,
s
=
50
∘
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C
p
=
45
∘
,
q
=
65
∘
,
r
=
50
∘
,
s
=
65
∘
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D
p
=
45
∘
,
q
=
50
∘
,
r
=
65
∘
,
s
=
65
∘
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Solution
The correct option is
A
p
=
45
∘
,
q
=
50
∘
,
r
=
65
∘
,
s
=
50
∘
In
Δ
A
B
C
,
r
=
180
∘
−
50
∘
−
65
∘
=
65
∘
[
angle sum property of a triangle
]
H
C
|
|
A
B
⇒
q
=
50
∘
[
Alternative angles
]
.
s = q [Vertically opposite angles]
Hence,
s
=
50
∘
Since BCF is a straight line,
(
p
+
20
∘
)
+
q
+
r
=
180
∘
⇒
p
=
45
∘
∴
p
=
45
∘
,
q
=
50
∘
,
r
=
65
∘
and
s
=
50
∘
are the required values.
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9
Similar questions
Q.
In the given figure, PQ is a diameter of a circle with centre O. If
∠PQR = 65°, ∠SPR = 40° and ∠PQM = 50°, find ∠QPR, ∠QPM and ∠PRS.