Question 45
Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are
a) $30^{\circ}, 150^{\circ}, 30^{\circ}, 150^{\circ}$
b) $85^{\circ}, 95^{\circ}, 85^{\circ}, 95^{\circ}$
c) $45^{\circ}, 135^{\circ}, 45^{\circ}, 135^{\circ}$
d) $30^{\circ}, 180^{\circ}, 30^{\circ}, 180^{\circ}$

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Solution

Let the adjacent angles of a parallelogram be x and 5x, respectively.
Then, $x + 5 x = 180^{\circ}$ [ $∵$ adjacent angles of a parallelogram are supplementary]
$\Rightarrow 6 x = 180^{\circ}$
$\Rightarrow x = 30^{\circ}$
$∴$ The adjacent anlges are $30^{\circ}$ and $150^{\circ}$ .
Hence, the angles are $30^{\circ}, 150^{\circ}, 30^{\circ}, 150^{\circ}$ . [ $∵$ opposite angles are equal]

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Q. Question 45
Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are
a)

30^{\circ}, 150^{\circ}, 30^{\circ}, 150^{\circ}

85^{\circ}, 95^{\circ}, 85^{\circ}, 95^{\circ}

45^{\circ}, 135^{\circ}, 45^{\circ}, 135^{\circ}

30^{\circ}, 180^{\circ}, 30^{\circ}, 180^{\circ}

Q. Question 5
Angles, which are both suplementary and vertically opposite are
(a)

95^{\circ}, 85^{\circ}

(b)

90^{\circ}, 90^{\circ}

(c)

100^{\circ}, 80^{\circ}

(d)

45^{\circ}, 45^{\circ}

The bisectors of any two adjacent angles of a parallelogram intersect at

(a) $30^{\circ}$

(b) $45^{\circ}$

(d) $90^{\circ}$

Question 5
Angles, which are both suplementary and vertically opposite are
(a) $95^{\circ}, 85^{\circ}$
(b) $90^{\circ}, 90^{\circ}$
(c) $100^{\circ}, 80^{\circ}$
(d) $45^{\circ}, 45^{\circ}$

Q. In a quadrilateral ABCD,

∠ A = 30^{\circ}, ∠ B = 150^{\circ}, ∠ C = 30^{\circ} and

∠ D = 150^{\circ}

Then ABCD is a

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Question 45 Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are a) 30∘,150∘,30∘,150∘ b) 85∘,95∘,85∘,95∘ c) 45∘,135∘,45∘,135∘ d) 30∘,180∘,30∘,180∘

Let the adjacent angles of a parallelogram be x and 5x, respectively. Then, x+5x=180∘ [∵ adjacent angles of a parallelogram are supplementary] ⇒6x=180∘ ⇒x=30∘ ∴ The adjacent anlges are 30∘ and 150∘. Hence, the angles are 30∘,150∘,30∘,150∘ . [∵ opposite angles are equal]