If the angles of a quadrilateral are in the ratio 2:5:4:7, then its smallest angle is equals to

40

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20

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80

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100

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Solution

The correct option is A $40$
Let $∠ A = 2 x, ∠ B = 5 x, ∠ C = 4 x a n d ∠ D = 7 x$
$∠ A + ∠ B + ∠ C + ∠ D = 360^{o}$ [ $∵$ sum of all the angles of quadrilateral is $360^{o}$ ]
$\Rightarrow 2 x + 5 x + 4 x + 7 x = 360^{o}$
$\Rightarrow 18 x = 360^{o}$
$\Rightarrow x = 20^{o}$
Smallest angle $= ∠ A = 2 x = 2 \times 20^{o} = 40^{o}$
Option A is correct.

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If the angles of a quadrilateral are in the ratio 2:5:4:7, then its smallest angle is equals to

The correct option is A 40Let ∠A=2x,∠B=5x,∠C=4xand∠D=7x∠A+∠B+∠C+∠D=360o [∵ sum of all the angles of quadrilateral is 360o]⇒2x+5x+4x+7x=360o ⇒18x=360o ⇒x=20o Smallest angle =∠A=2x=2×20o=40oOption A is correct.