Quadrilateral || Shashaank Blogspot

The angles of a quadrilateral are in the ratio $2 : 3 : 5 : 8$ . Find the smallest angle of the quadrilateral?

Given ratio of angles of quadrilateral $A B C D$ is $2 : 3 : 5 : 8$
Let the angles of quadrilateral $A B C D$ be $2 x, 3 x, 5 x, 8 x$ , respectively.
We know, by angle sum property, the sum of angles of a quadrilateral is $36 0^{o}$ .
$\Rightarrow 2 x + 3 x + 5 x + 8 x = 36 0^{o}$
$\Rightarrow 18 x = 36 0^{o}$
$∴ x = 2 0^{o}$ .
$∴ ∠ A = 2 x = 2 \times 2 0^{o} = 4 0^{o}$ ,
$∠ B = 3 x = 3 \times 2 0^{o} = 6 0^{o}$ ,
$∠ C = 5 x = 5 \times 2 0^{o} = 10 0^{o}$
and $∠ D = 8 x = 8 \times 2 0^{o} = 16 0^{o}$ .
$∴$ The smallest angle $= 40$

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