The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.

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Solution

The angles of a quadrilateral are in the ratio 3:4:5:6.

Let the angles of the quadrilateral be $3 x, 4 x, 5 x, 6 x$ .

The sum of the angles of a quadrilateral is $360^{\circ}$ .
$\Rightarrow 3 x + 4 x + 5 x + 6 x = 360^{\circ}$
$\Rightarrow 18 x = 360^{\circ}$
$\Rightarrow x = 20^{\circ}$

$∴ 3 x = 60^{\circ}, 4 x = 80^{\circ}, 5 x = 100^{\circ}, a n d 6 x = 120^{\circ}$

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