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Byju's Answer
Standard IX
Mathematics
Converse of Theorem 3
In a quadrila...
Question
In a quadrilateral ABCD,
∠
A
=
30
∘
,
∠
B
=
150
∘
,
∠
C
=
30
∘
and
∠
D
=
150
∘
Then ABCD is a
A
Rectangle
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B
Trapezium
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C
Kite
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D
Parallelogram
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Solution
The correct option is
D
Parallelogram
In ABCD the pairs of oppposite angles of ABCD are equal. So, ABCD is a parallelogram.
Among the options, the quadrilateral ABCD can be either 'Rectangle' or 'Parallelogram'. [
∵
Rectangle is also a parallelogram]
In rectangle all angles are of
90
∘
but in the quadrilateral ABCD all angles are not equal to
90
∘
. So, ABCD is not a rectangle.
Hence, ABCD is a parallelogram
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Similar questions
Q.
ABCD is a cyclic quadrilateral such that ∠ADB = 30° and ∠DCA = 80°, then ∠DAB =
(a) 70°
(b) 100°
(c) 125°
(d) 150°