Question

Find the four angles of quadrilateral, if the angles are in the ratios:
$2:3:4:6$

Answer 1

By the angle sum property, sum of all interior angles in a quadrilateral $={360}^{\circ }$

Let $2x,3x,4x,6x$ be the interior angles in a quadrilateral.

Then,

$\Rightarrow 2x+3x+4x+6x={360}^{\circ }$

$\Rightarrow 15x={360}^{\circ }$

$\Rightarrow x=\frac{{360}^{\circ }}{15}={24}^{\circ }$

$\therefore 2x=2\times {24}^{\circ }={48}^{\circ }$

$3x=3\times {24}^{\circ }={72}^{\circ }$

$4x=4\times {24}^{\circ }={96}^{\circ }$

$6x=6\times {24}^{\circ }={144}^{\circ }$

$\therefore$ the interior angles in a given quadrilateral is ${48}^{\circ },{72}^{\circ },{96}^{\circ }$ and ${144}^{\circ }$