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Byju's Answer
Standard VIII
Mathematics
Rhombus
PQRS is a rho...
Question
P
Q
R
S
is a rhombus with
∠
P
Q
R
=
54
∘
. Determine
∠
P
R
S
A
∠
P
R
S
=
53
∘
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B
∠
P
R
S
=
63
∘
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C
∠
P
R
S
=
73
∘
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D
∠
P
R
S
=
83
∘
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Solution
The correct option is
C
∠
P
R
S
=
63
∘
Given that
P
Q
R
S
is a rhombus
∠
P
S
R
=
∠
P
Q
R
=
54
∘
(opp.
∠
S
of a rhombus are equal)
⇒
∠
O
S
R
=
1
2
×
∠
P
S
R
=
1
2
×
54
∘
=
27
∘
(
S
Q
bisects
∠
P
S
R
)
Now in
Δ
O
S
R
∠
O
R
S
+
∠
R
O
S
+
∠
O
S
R
=
180
∘
⇒
∠
O
R
S
+
27
∘
+
90
∘
=
180
∘
(Diagonals of a rhombus bisect each other at right
∠
s
)
⇒
∠
O
R
S
=
63
∘
⇒
∠
P
R
S
=
63
∘
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Similar questions
Q.
P
Q
R
S
is a rhombus with
∠
P
Q
R
=
58
o
. Determine
∠
P
R
S
.
Q.
In the figure given below,
∠
P
Q
R
=
∠
P
R
S
. Prove that triangles
P
Q
R
and
P
R
S
are similar. If
P
R
=
8
c
m
,
P
S
=
4
c
m
, calculate
P
Q
.
Q.
PQRS is a parallelogram whose diagonals intersect at M.
If
∠
P
M
S
=
54
∘
,
∠
Q
S
R
=
25
∘
and
∠
S
Q
R
=
30
∘
: find
∠
P
R
S
Q.
If PQRS is a parallelogram with PR
=
QS, and PR is perpendicular to QS,then PQRS is a
Q.
Question 9
In
Δ
P
Q
R
,
a) PQ - QR > PR
b) PQ + QR < PR
c) PQ - QR < PR
d) PQ + PR < QR
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