Question

The angles of a quadrilateral are in the ratio $2:4:5:7.$ Find the angles.

Answer 1

Sum of the angles if a quadrilateral is ${360}^{\circ }$.

the ratio of angles $=2:4:5:7$

Let the angles be $2x,4x,5x,7x$

So $2x+4x+5x+7x={360}^{\circ }$

$\Rightarrow 18x={360}^{\circ }$

$\Rightarrow x={\frac{360}{18}}^{\circ }$

$\therefore x={20}^{\circ }$

So $1$st angle $=2x=2\times {20}^{\circ }={40}^{\circ }$
$2$nd angle $=4x=4\times {20}^{\circ }={80}^{\circ }$
$3$rd angle $=5x=5\times {20}^{\circ }={100}^{\circ }$
$4$th angle $=7x=7\times {20}^{\circ }={140}^{\circ }$