Question

If the angles of a quadrilateral are in the ratio $1:2:3:4$ find the angles

Answer 1

Ratio of the angles $1:2:3:4$
Let the angles be $x,2x,3x$ and $4x$
$x+2x+3x+4x={360}^o$
[ Angle sum property of a quadrilateral]
$10x={360}^o$
$x=\frac{360}{10};x={36}^o$
$2x=2\times 36={72}^o,3x=3\times 36={108}^o$
$4x=4\times 36={144}^o$
$\therefore$ The angles are ${36}^o,{72}^o,{108}^o$ and ${144}^o$