Question

Angles of a quadrilateral are in the ratio $1:2:3:4$ Find all the angles.

Answer 1

Given:

Angles of a quadrilateral are in the ratio $1:2:3:4$.

Sot the angles be $x,2x,3x,$ ans $4x$.

Since, sum of angles of a quadrilateral is ${360}^{\circ }$ .

$\Rightarrow x+2x+3x+4x={360}^{\circ }$

$\Rightarrow 10x={360}^{\circ }$

$\Rightarrow x={36}^{\circ }$

So, angles are:

$x={36}^{\circ }$

$2x=2\times {36}^{\circ }={72}^{\circ }$

$3x=3\times {36}^{\circ }={108}^{\circ }$

$4x=4\times {36}^{\circ }={144}^{\circ }$

Therefore, the angles of the quadrilateral are ${36}^{\circ },{72}^{\circ },{108}^{\circ }$ and ${144}^{\circ }$.