The angles of a quadrilateral are in the ratio 1: 2 : 3 : 4. The angles of the quadrilateral are respectively ____. Options: A . &nbsp 144 ∘ , 108 ∘ , 60 ∘ , 48 ∘ B . &nbsp 36 ∘ , 72 ∘ , 108 ∘ , 144 ∘ C . &nbsp 30 ∘ , 60 ∘ , 90 ∘ , 120 ∘ D . &nbsp 10 ∘ , 20 ∘ , 30 ∘ , 40 ∘

Answer: Option B : B Let the smallest angle of quadrilateral be x ∘ . Then, the angles of the quadrilateral will be x ∘ , 2 x ∘ , 3 x ∘ and 4 x ∘ . Sum of the angles of a quadrilateral is 360 ∘ . ⇒ 360 ∘ = x + 2 x + 3 x + 4 x ⇒ 10 x = 360 ∘ ∴ x = 36 ∘ , 2 x = 72 ∘ , 3 x = 108 ∘ a n d 4 x = 144 ∘

The angles of a quadrilateral are in the ratio 1: 2 : 3 : 4. The angles of the

Question

The angles of a quadrilateral are in the ratio 1: 2 : 3 : 4. The angles of the quadrilateral are respectively ____.

Options:

A .

144^{\circ}

108^{\circ}

60^{\circ}

48^{\circ}

B .

36^{\circ}

72^{\circ}

108^{\circ}

144^{\circ}

C .

30^{\circ}

60^{\circ}

90^{\circ}

120^{\circ}

D .

10^{\circ}

20^{\circ}

30^{\circ}

40^{\circ}

Answer: Option B
:
B

Let the smallest angle of quadrilateral be $x^{\circ}$ .
Then, the angles of the quadrilateral will be $x^{\circ}$ , $2 x^{\circ}$ , $3 x^{\circ}$ and $4 x^{\circ}$ .
Sum of the angles of a quadrilateral is $360^{\circ}$ .
$\Rightarrow 360^{\circ} = x + 2 x + 3 x + 4 x$
$\Rightarrow 10 x = 360^{\circ}$
$∴ x = 36^{\circ}, 2 x = 72^{\circ}, 3 x = 108^{\circ} a n d 4 x = 144^{\circ}$

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