The angles of a quadrilateral cannot be in the ratio $1 : 2 : 3 : 6$ . Why? Give reasons.

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Solution

Let the angles be $x, 2 x, 3 x, 6 x$
Sum of angles in a quadrilateral is $360^{\circ}$
$x + 2 x + 3 x + 6 x = 360^{\circ}$
$12 x = 360^{\circ}$
$x = 30^{\circ}$
$6 x = 180^{\circ}$ which is not possible

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